F2c: Separation of variables

Example 1

F2c: Separation of variables (ver. 1)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= -2\]

Answer.

\[y= -2 \, \sin\left(3 \, t\right)\]

Example 2

F2c: Separation of variables (ver. 2)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -1\]

Answer.

\[y= -\cos\left(3 \, t\right)\]

Example 3

F2c: Separation of variables (ver. 3)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= -4\]

Answer.

\[y= -4 \, \sin\left(2 \, t\right)\]

Example 4

F2c: Separation of variables (ver. 4)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= 1\]

Answer.

\[y= \cos\left(2 \, t\right)\]

Example 5

F2c: Separation of variables (ver. 5)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= -1\]

Answer.

\[y= -\sin\left(t\right)\]

Example 6

F2c: Separation of variables (ver. 6)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= -2\]

Answer.

\[y= -2 \, \sin\left(3 \, t\right)\]

Example 7

F2c: Separation of variables (ver. 7)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= 3\]

Answer.

\[y= 3 \, \sin\left(3 \, t\right)\]

Example 8

F2c: Separation of variables (ver. 8)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= -3\]

Answer.

\[y= -3 \, \sin\left(3 \, t\right)\]

Example 9

F2c: Separation of variables (ver. 9)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= -3\]

Answer.

\[y= -3 \, \cos\left(2 \, t\right)\]

Example 10

F2c: Separation of variables (ver. 10)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -2\]

Answer.

\[y= -2 \, \cos\left(3 \, t\right)\]

Example 11

F2c: Separation of variables (ver. 11)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= -1\]

Answer.

\[y= -\cos\left(2 \, t\right)\]

Example 12

F2c: Separation of variables (ver. 12)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 2\]

Answer.

\[y= 2 \, \sin\left(2 \, t\right)\]

Example 13

F2c: Separation of variables (ver. 13)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= 1\]

Answer.

\[y= \sin\left(t\right)\]

Example 14

F2c: Separation of variables (ver. 14)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= -4\]

Answer.

\[y= -4 \, \cos\left(t\right)\]

Example 15

F2c: Separation of variables (ver. 15)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= 1\]

Answer.

\[y= \sin\left(3 \, t\right)\]

Example 16

F2c: Separation of variables (ver. 16)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 1\]

Answer.

\[y= \sin\left(2 \, t\right)\]

Example 17

F2c: Separation of variables (ver. 17)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= 2\]

Answer.

\[y= 2 \, \cos\left(2 \, t\right)\]

Example 18

F2c: Separation of variables (ver. 18)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -3\]

Answer.

\[y= -3 \, \cos\left(3 \, t\right)\]

Example 19

F2c: Separation of variables (ver. 19)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 4\]

Answer.

\[y= 4 \, \sin\left(2 \, t\right)\]

Example 20

F2c: Separation of variables (ver. 20)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 3\]

Answer.

\[y= 3 \, \sin\left(2 \, t\right)\]

Example 21

F2c: Separation of variables (ver. 21)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= 1\]

Answer.

\[y= \cos\left(t\right)\]

Example 22

F2c: Separation of variables (ver. 22)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= -1\]

Answer.

\[y= -\cos\left(t\right)\]

Example 23

F2c: Separation of variables (ver. 23)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= -1\]

Answer.

\[y= -\cos\left(t\right)\]

Example 24

F2c: Separation of variables (ver. 24)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 2\]

Answer.

\[y= 2 \, \sin\left(2 \, t\right)\]

Example 25

F2c: Separation of variables (ver. 25)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 4\]

Answer.

\[y= 4 \, \sin\left(2 \, t\right)\]

Example 26

F2c: Separation of variables (ver. 26)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= 1\]

Answer.

\[y= \sin\left(3 \, t\right)\]

Example 27

F2c: Separation of variables (ver. 27)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= -4\]

Answer.

\[y= -4 \, \sin\left(t\right)\]

Example 28

F2c: Separation of variables (ver. 28)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= -4\]

Answer.

\[y= -4 \, \sin\left(2 \, t\right)\]

Example 29

F2c: Separation of variables (ver. 29)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= -2\]

Answer.

\[y= -2 \, \sin\left(3 \, t\right)\]

Example 30

F2c: Separation of variables (ver. 30)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 1\]

Answer.

\[y= \sin\left(2 \, t\right)\]

Example 31

F2c: Separation of variables (ver. 31)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= -3\]

Answer.

\[y= -3 \, \sin\left(t\right)\]

Example 32

F2c: Separation of variables (ver. 32)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 4\]

Answer.

\[y= 4 \, \sin\left(2 \, t\right)\]

Example 33

F2c: Separation of variables (ver. 33)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= 4\]

Answer.

\[y= 4 \, \cos\left(t\right)\]

Example 34

F2c: Separation of variables (ver. 34)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= -2\]

Answer.

\[y= -2 \, \sin\left(2 \, t\right)\]

Example 35

F2c: Separation of variables (ver. 35)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= 3\]

Answer.

\[y= 3 \, \sin\left(t\right)\]

Example 36

F2c: Separation of variables (ver. 36)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -3\]

Answer.

\[y= -3 \, \cos\left(3 \, t\right)\]

Example 37

F2c: Separation of variables (ver. 37)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= -4\]

Answer.

\[y= -4 \, \sin\left(3 \, t\right)\]

Example 38

F2c: Separation of variables (ver. 38)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= 1\]

Answer.

\[y= \cos\left(t\right)\]

Example 39

F2c: Separation of variables (ver. 39)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -3\]

Answer.

\[y= -3 \, \cos\left(3 \, t\right)\]

Example 40

F2c: Separation of variables (ver. 40)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= -1\]

Answer.

\[y= -\cos\left(2 \, t\right)\]

Example 41

F2c: Separation of variables (ver. 41)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= -4\]

Answer.

\[y= -4 \, \sin\left(t\right)\]

Example 42

F2c: Separation of variables (ver. 42)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 4\]

Answer.

\[y= 4 \, \sin\left(2 \, t\right)\]

Example 43

F2c: Separation of variables (ver. 43)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= 2\]

Answer.

\[y= 2 \, \sin\left(t\right)\]

Example 44

F2c: Separation of variables (ver. 44)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= -1\]

Answer.

\[y= -\cos\left(t\right)\]

Example 45

F2c: Separation of variables (ver. 45)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= 1\]

Answer.

\[y= \sin\left(3 \, t\right)\]

Example 46

F2c: Separation of variables (ver. 46)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= -2\]

Answer.

\[y= -2 \, \sin\left(2 \, t\right)\]

Example 47

F2c: Separation of variables (ver. 47)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -1\]

Answer.

\[y= -\cos\left(3 \, t\right)\]

Example 48

F2c: Separation of variables (ver. 48)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= 3\]

Answer.

\[y= 3 \, \sin\left(t\right)\]

Example 49

F2c: Separation of variables (ver. 49)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= -1\]

Answer.

\[y= -\cos\left(2 \, t\right)\]

Example 50

F2c: Separation of variables (ver. 50)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= 4\]

Answer.

\[y= 4 \, \cos\left(2 \, t\right)\]

Example 51

F2c: Separation of variables (ver. 51)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= 3\]

Answer.

\[y= 3 \, \cos\left(t\right)\]

Example 52

F2c: Separation of variables (ver. 52)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 3\]

Answer.

\[y= 3 \, \sin\left(2 \, t\right)\]

Example 53

F2c: Separation of variables (ver. 53)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= -4\]

Answer.

\[y= -4 \, \sin\left(3 \, t\right)\]

Example 54

F2c: Separation of variables (ver. 54)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= 3\]

Answer.

\[y= 3 \, \sin\left(3 \, t\right)\]

Example 55

F2c: Separation of variables (ver. 55)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= -1\]

Answer.

\[y= -\sin\left(3 \, t\right)\]

Example 56

F2c: Separation of variables (ver. 56)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= 3\]

Answer.

\[y= 3 \, \cos\left(2 \, t\right)\]

Example 57

F2c: Separation of variables (ver. 57)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= 4\]

Answer.

\[y= 4 \, \cos\left(3 \, t\right)\]

Example 58

F2c: Separation of variables (ver. 58)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= -2\]

Answer.

\[y= -2 \, \cos\left(2 \, t\right)\]

Example 59

F2c: Separation of variables (ver. 59)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= -4\]

Answer.

\[y= -4 \, \cos\left(t\right)\]

Example 60

F2c: Separation of variables (ver. 60)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= -1\]

Answer.

\[y= -\cos\left(t\right)\]

Example 61

F2c: Separation of variables (ver. 61)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= 2\]

Answer.

\[y= 2 \, \sin\left(t\right)\]

Example 62

F2c: Separation of variables (ver. 62)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= 2\]

Answer.

\[y= 2 \, \cos\left(t\right)\]

Example 63

F2c: Separation of variables (ver. 63)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= 2\]

Answer.

\[y= 2 \, \cos\left(3 \, t\right)\]

Example 64

F2c: Separation of variables (ver. 64)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= 1\]

Answer.

\[y= \sin\left(3 \, t\right)\]

Example 65

F2c: Separation of variables (ver. 65)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -3\]

Answer.

\[y= -3 \, \cos\left(3 \, t\right)\]

Example 66

F2c: Separation of variables (ver. 66)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= -4\]

Answer.

\[y= -4 \, \cos\left(2 \, t\right)\]

Example 67

F2c: Separation of variables (ver. 67)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= -4\]

Answer.

\[y= -4 \, \sin\left(3 \, t\right)\]

Example 68

F2c: Separation of variables (ver. 68)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= 4\]

Answer.

\[y= 4 \, \sin\left(t\right)\]

Example 69

F2c: Separation of variables (ver. 69)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= -2\]

Answer.

\[y= -2 \, \sin\left(2 \, t\right)\]

Example 70

F2c: Separation of variables (ver. 70)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= 1\]

Answer.

\[y= \cos\left(3 \, t\right)\]

Example 71

F2c: Separation of variables (ver. 71)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -4\]

Answer.

\[y= -4 \, \cos\left(3 \, t\right)\]

Example 72

F2c: Separation of variables (ver. 72)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= -3\]

Answer.

\[y= -3 \, \sin\left(3 \, t\right)\]

Example 73

F2c: Separation of variables (ver. 73)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= 2\]

Answer.

\[y= 2 \, \sin\left(3 \, t\right)\]

Example 74

F2c: Separation of variables (ver. 74)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= -3\]

Answer.

\[y= -3 \, \sin\left(t\right)\]

Example 75

F2c: Separation of variables (ver. 75)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= -4\]

Answer.

\[y= -4 \, \cos\left(2 \, t\right)\]

Example 76

F2c: Separation of variables (ver. 76)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= 4\]

Answer.

\[y= 4 \, \sin\left(3 \, t\right)\]

Example 77

F2c: Separation of variables (ver. 77)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= 4\]

Answer.

\[y= 4 \, \sin\left(3 \, t\right)\]

Example 78

F2c: Separation of variables (ver. 78)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= -3\]

Answer.

\[y= -3 \, \sin\left(t\right)\]

Example 79

F2c: Separation of variables (ver. 79)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= -2\]

Answer.

\[y= -2 \, \cos\left(t\right)\]

Example 80

F2c: Separation of variables (ver. 80)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= -1\]

Answer.

\[y= -\sin\left(3 \, t\right)\]

Example 81

F2c: Separation of variables (ver. 81)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -3\]

Answer.

\[y= -3 \, \cos\left(3 \, t\right)\]

Example 82

F2c: Separation of variables (ver. 82)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -1\]

Answer.

\[y= -\cos\left(3 \, t\right)\]

Example 83

F2c: Separation of variables (ver. 83)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= -2\]

Answer.

\[y= -2 \, \cos\left(t\right)\]

Example 84

F2c: Separation of variables (ver. 84)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -3\]

Answer.

\[y= -3 \, \cos\left(3 \, t\right)\]

Example 85

F2c: Separation of variables (ver. 85)

Find the solution to the given IVP.

\[-2 \, \sin\left(2 \, t\right) y= \cos\left(2 \, t\right) y'\hspace{1em} y\left( 0 \right)= -3\]

Answer.

\[y= -3 \, \cos\left(2 \, t\right)\]

Example 86

F2c: Separation of variables (ver. 86)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= 2\]

Answer.

\[y= 2 \, \cos\left(t\right)\]

Example 87

F2c: Separation of variables (ver. 87)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 4\]

Answer.

\[y= 4 \, \sin\left(2 \, t\right)\]

Example 88

F2c: Separation of variables (ver. 88)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= 2\]

Answer.

\[y= 2 \, \cos\left(3 \, t\right)\]

Example 89

F2c: Separation of variables (ver. 89)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= 3\]

Answer.

\[y= 3 \, \cos\left(3 \, t\right)\]

Example 90

F2c: Separation of variables (ver. 90)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= 1\]

Answer.

\[y= \sin\left(2 \, t\right)\]

Example 91

F2c: Separation of variables (ver. 91)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= -3\]

Answer.

\[y= -3 \, \cos\left(3 \, t\right)\]

Example 92

F2c: Separation of variables (ver. 92)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= -1\]

Answer.

\[y= -\sin\left(t\right)\]

Example 93

F2c: Separation of variables (ver. 93)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= -3\]

Answer.

\[y= -3 \, \sin\left(t\right)\]

Example 94

F2c: Separation of variables (ver. 94)

Find the solution to the given IVP.

\[-3 \, \sin\left(3 \, t\right) y= \cos\left(3 \, t\right) y'\hspace{1em} y\left( 0 \right)= 3\]

Answer.

\[y= 3 \, \cos\left(3 \, t\right)\]

Example 95

F2c: Separation of variables (ver. 95)

Find the solution to the given IVP.

\[\cos\left(t\right) y= \sin\left(t\right) y'\hspace{1em} y\left( \frac{1}{2} \, \pi \right)= -4\]

Answer.

\[y= -4 \, \sin\left(t\right)\]

Example 96

F2c: Separation of variables (ver. 96)

Find the solution to the given IVP.

\[3 \, \cos\left(3 \, t\right) y= \sin\left(3 \, t\right) y'\hspace{1em} y\left( \frac{1}{6} \, \pi \right)= 2\]

Answer.

\[y= 2 \, \sin\left(3 \, t\right)\]

Example 97

F2c: Separation of variables (ver. 97)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= 4\]

Answer.

\[y= 4 \, \cos\left(t\right)\]

Example 98

F2c: Separation of variables (ver. 98)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= -2\]

Answer.

\[y= -2 \, \cos\left(t\right)\]

Example 99

F2c: Separation of variables (ver. 99)

Find the solution to the given IVP.

\[-\sin\left(t\right) y= \cos\left(t\right) y'\hspace{1em} y\left( 0 \right)= 2\]

Answer.

\[y= 2 \, \cos\left(t\right)\]

Example 100

F2c: Separation of variables (ver. 100)

Find the solution to the given IVP.

\[2 \, \cos\left(2 \, t\right) y= \sin\left(2 \, t\right) y'\hspace{1em} y\left( \frac{1}{4} \, \pi \right)= -1\]

Answer.

\[y= -\sin\left(2 \, t\right)\]