C1 - Homogeneous first-order linear ODE

Example 1

C1 - Homogeneous first-order linear ODE (ver. 1)

Find the general solution to the given ODE.

\[y'-8y=0\]

Answer.

\[y= k e^{\left(8 \, t\right)}\]

Example 2

C1 - Homogeneous first-order linear ODE (ver. 2)

Find the general solution to the given ODE.

\[y'+9y=0\]

Answer.

\[y= k e^{\left(-9 \, t\right)}\]

Example 3

C1 - Homogeneous first-order linear ODE (ver. 3)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]

Example 4

C1 - Homogeneous first-order linear ODE (ver. 4)

Find the general solution to the given ODE.

\[y'+6y=0\]

Answer.

\[y= k e^{\left(-6 \, t\right)}\]

Example 5

C1 - Homogeneous first-order linear ODE (ver. 5)

Find the general solution to the given ODE.

\[y'-1y=0\]

Answer.

\[y= k e^{t}\]

Example 6

C1 - Homogeneous first-order linear ODE (ver. 6)

Find the general solution to the given ODE.

\[y'-9y=0\]

Answer.

\[y= k e^{\left(9 \, t\right)}\]

Example 7

C1 - Homogeneous first-order linear ODE (ver. 7)

Find the general solution to the given ODE.

\[y'-8y=0\]

Answer.

\[y= k e^{\left(8 \, t\right)}\]

Example 8

C1 - Homogeneous first-order linear ODE (ver. 8)

Find the general solution to the given ODE.

\[y'-8y=0\]

Answer.

\[y= k e^{\left(8 \, t\right)}\]

Example 9

C1 - Homogeneous first-order linear ODE (ver. 9)

Find the general solution to the given ODE.

\[y'+6y=0\]

Answer.

\[y= k e^{\left(-6 \, t\right)}\]

Example 10

C1 - Homogeneous first-order linear ODE (ver. 10)

Find the general solution to the given ODE.

\[y'+9y=0\]

Answer.

\[y= k e^{\left(-9 \, t\right)}\]

Example 11

C1 - Homogeneous first-order linear ODE (ver. 11)

Find the general solution to the given ODE.

\[y'+5y=0\]

Answer.

\[y= k e^{\left(-5 \, t\right)}\]

Example 12

C1 - Homogeneous first-order linear ODE (ver. 12)

Find the general solution to the given ODE.

\[y'-5y=0\]

Answer.

\[y= k e^{\left(5 \, t\right)}\]

Example 13

C1 - Homogeneous first-order linear ODE (ver. 13)

Find the general solution to the given ODE.

\[y'-3y=0\]

Answer.

\[y= k e^{\left(3 \, t\right)}\]

Example 14

C1 - Homogeneous first-order linear ODE (ver. 14)

Find the general solution to the given ODE.

\[y'+y=0\]

Answer.

\[y= k e^{\left(-t\right)}\]

Example 15

C1 - Homogeneous first-order linear ODE (ver. 15)

Find the general solution to the given ODE.

\[y'-7y=0\]

Answer.

\[y= k e^{\left(7 \, t\right)}\]

Example 16

C1 - Homogeneous first-order linear ODE (ver. 16)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]

Example 17

C1 - Homogeneous first-order linear ODE (ver. 17)

Find the general solution to the given ODE.

\[y'+5y=0\]

Answer.

\[y= k e^{\left(-5 \, t\right)}\]

Example 18

C1 - Homogeneous first-order linear ODE (ver. 18)

Find the general solution to the given ODE.

\[y'+9y=0\]

Answer.

\[y= k e^{\left(-9 \, t\right)}\]

Example 19

C1 - Homogeneous first-order linear ODE (ver. 19)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]

Example 20

C1 - Homogeneous first-order linear ODE (ver. 20)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]

Example 21

C1 - Homogeneous first-order linear ODE (ver. 21)

Find the general solution to the given ODE.

\[y'+3y=0\]

Answer.

\[y= k e^{\left(-3 \, t\right)}\]

Example 22

C1 - Homogeneous first-order linear ODE (ver. 22)

Find the general solution to the given ODE.

\[y'+3y=0\]

Answer.

\[y= k e^{\left(-3 \, t\right)}\]

Example 23

C1 - Homogeneous first-order linear ODE (ver. 23)

Find the general solution to the given ODE.

\[y'+y=0\]

Answer.

\[y= k e^{\left(-t\right)}\]

Example 24

C1 - Homogeneous first-order linear ODE (ver. 24)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]

Example 25

C1 - Homogeneous first-order linear ODE (ver. 25)

Find the general solution to the given ODE.

\[y'-5y=0\]

Answer.

\[y= k e^{\left(5 \, t\right)}\]

Example 26

C1 - Homogeneous first-order linear ODE (ver. 26)

Find the general solution to the given ODE.

\[y'-9y=0\]

Answer.

\[y= k e^{\left(9 \, t\right)}\]

Example 27

C1 - Homogeneous first-order linear ODE (ver. 27)

Find the general solution to the given ODE.

\[y'-2y=0\]

Answer.

\[y= k e^{\left(2 \, t\right)}\]

Example 28

C1 - Homogeneous first-order linear ODE (ver. 28)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]

Example 29

C1 - Homogeneous first-order linear ODE (ver. 29)

Find the general solution to the given ODE.

\[y'-8y=0\]

Answer.

\[y= k e^{\left(8 \, t\right)}\]

Example 30

C1 - Homogeneous first-order linear ODE (ver. 30)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]

Example 31

C1 - Homogeneous first-order linear ODE (ver. 31)

Find the general solution to the given ODE.

\[y'-1y=0\]

Answer.

\[y= k e^{t}\]

Example 32

C1 - Homogeneous first-order linear ODE (ver. 32)

Find the general solution to the given ODE.

\[y'-5y=0\]

Answer.

\[y= k e^{\left(5 \, t\right)}\]

Example 33

C1 - Homogeneous first-order linear ODE (ver. 33)

Find the general solution to the given ODE.

\[y'+y=0\]

Answer.

\[y= k e^{\left(-t\right)}\]

Example 34

C1 - Homogeneous first-order linear ODE (ver. 34)

Find the general solution to the given ODE.

\[y'-6y=0\]

Answer.

\[y= k e^{\left(6 \, t\right)}\]

Example 35

C1 - Homogeneous first-order linear ODE (ver. 35)

Find the general solution to the given ODE.

\[y'-3y=0\]

Answer.

\[y= k e^{\left(3 \, t\right)}\]

Example 36

C1 - Homogeneous first-order linear ODE (ver. 36)

Find the general solution to the given ODE.

\[y'+8y=0\]

Answer.

\[y= k e^{\left(-8 \, t\right)}\]

Example 37

C1 - Homogeneous first-order linear ODE (ver. 37)

Find the general solution to the given ODE.

\[y'-7y=0\]

Answer.

\[y= k e^{\left(7 \, t\right)}\]

Example 38

C1 - Homogeneous first-order linear ODE (ver. 38)

Find the general solution to the given ODE.

\[y'+2y=0\]

Answer.

\[y= k e^{\left(-2 \, t\right)}\]

Example 39

C1 - Homogeneous first-order linear ODE (ver. 39)

Find the general solution to the given ODE.

\[y'+8y=0\]

Answer.

\[y= k e^{\left(-8 \, t\right)}\]

Example 40

C1 - Homogeneous first-order linear ODE (ver. 40)

Find the general solution to the given ODE.

\[y'+4y=0\]

Answer.

\[y= k e^{\left(-4 \, t\right)}\]

Example 41

C1 - Homogeneous first-order linear ODE (ver. 41)

Find the general solution to the given ODE.

\[y'-3y=0\]

Answer.

\[y= k e^{\left(3 \, t\right)}\]

Example 42

C1 - Homogeneous first-order linear ODE (ver. 42)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]

Example 43

C1 - Homogeneous first-order linear ODE (ver. 43)

Find the general solution to the given ODE.

\[y'-2y=0\]

Answer.

\[y= k e^{\left(2 \, t\right)}\]

Example 44

C1 - Homogeneous first-order linear ODE (ver. 44)

Find the general solution to the given ODE.

\[y'+y=0\]

Answer.

\[y= k e^{\left(-t\right)}\]

Example 45

C1 - Homogeneous first-order linear ODE (ver. 45)

Find the general solution to the given ODE.

\[y'-8y=0\]

Answer.

\[y= k e^{\left(8 \, t\right)}\]

Example 46

C1 - Homogeneous first-order linear ODE (ver. 46)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]

Example 47

C1 - Homogeneous first-order linear ODE (ver. 47)

Find the general solution to the given ODE.

\[y'+8y=0\]

Answer.

\[y= k e^{\left(-8 \, t\right)}\]

Example 48

C1 - Homogeneous first-order linear ODE (ver. 48)

Find the general solution to the given ODE.

\[y'-2y=0\]

Answer.

\[y= k e^{\left(2 \, t\right)}\]

Example 49

C1 - Homogeneous first-order linear ODE (ver. 49)

Find the general solution to the given ODE.

\[y'+5y=0\]

Answer.

\[y= k e^{\left(-5 \, t\right)}\]

Example 50

C1 - Homogeneous first-order linear ODE (ver. 50)

Find the general solution to the given ODE.

\[y'+6y=0\]

Answer.

\[y= k e^{\left(-6 \, t\right)}\]

Example 51

C1 - Homogeneous first-order linear ODE (ver. 51)

Find the general solution to the given ODE.

\[y'+3y=0\]

Answer.

\[y= k e^{\left(-3 \, t\right)}\]

Example 52

C1 - Homogeneous first-order linear ODE (ver. 52)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]

Example 53

C1 - Homogeneous first-order linear ODE (ver. 53)

Find the general solution to the given ODE.

\[y'-7y=0\]

Answer.

\[y= k e^{\left(7 \, t\right)}\]

Example 54

C1 - Homogeneous first-order linear ODE (ver. 54)

Find the general solution to the given ODE.

\[y'-7y=0\]

Answer.

\[y= k e^{\left(7 \, t\right)}\]

Example 55

C1 - Homogeneous first-order linear ODE (ver. 55)

Find the general solution to the given ODE.

\[y'-9y=0\]

Answer.

\[y= k e^{\left(9 \, t\right)}\]

Example 56

C1 - Homogeneous first-order linear ODE (ver. 56)

Find the general solution to the given ODE.

\[y'+6y=0\]

Answer.

\[y= k e^{\left(-6 \, t\right)}\]

Example 57

C1 - Homogeneous first-order linear ODE (ver. 57)

Find the general solution to the given ODE.

\[y'+7y=0\]

Answer.

\[y= k e^{\left(-7 \, t\right)}\]

Example 58

C1 - Homogeneous first-order linear ODE (ver. 58)

Find the general solution to the given ODE.

\[y'+6y=0\]

Answer.

\[y= k e^{\left(-6 \, t\right)}\]

Example 59

C1 - Homogeneous first-order linear ODE (ver. 59)

Find the general solution to the given ODE.

\[y'+2y=0\]

Answer.

\[y= k e^{\left(-2 \, t\right)}\]

Example 60

C1 - Homogeneous first-order linear ODE (ver. 60)

Find the general solution to the given ODE.

\[y'+3y=0\]

Answer.

\[y= k e^{\left(-3 \, t\right)}\]

Example 61

C1 - Homogeneous first-order linear ODE (ver. 61)

Find the general solution to the given ODE.

\[y'-1y=0\]

Answer.

\[y= k e^{t}\]

Example 62

C1 - Homogeneous first-order linear ODE (ver. 62)

Find the general solution to the given ODE.

\[y'+y=0\]

Answer.

\[y= k e^{\left(-t\right)}\]

Example 63

C1 - Homogeneous first-order linear ODE (ver. 63)

Find the general solution to the given ODE.

\[y'+8y=0\]

Answer.

\[y= k e^{\left(-8 \, t\right)}\]

Example 64

C1 - Homogeneous first-order linear ODE (ver. 64)

Find the general solution to the given ODE.

\[y'-9y=0\]

Answer.

\[y= k e^{\left(9 \, t\right)}\]

Example 65

C1 - Homogeneous first-order linear ODE (ver. 65)

Find the general solution to the given ODE.

\[y'+7y=0\]

Answer.

\[y= k e^{\left(-7 \, t\right)}\]

Example 66

C1 - Homogeneous first-order linear ODE (ver. 66)

Find the general solution to the given ODE.

\[y'+5y=0\]

Answer.

\[y= k e^{\left(-5 \, t\right)}\]

Example 67

C1 - Homogeneous first-order linear ODE (ver. 67)

Find the general solution to the given ODE.

\[y'-9y=0\]

Answer.

\[y= k e^{\left(9 \, t\right)}\]

Example 68

C1 - Homogeneous first-order linear ODE (ver. 68)

Find the general solution to the given ODE.

\[y'-2y=0\]

Answer.

\[y= k e^{\left(2 \, t\right)}\]

Example 69

C1 - Homogeneous first-order linear ODE (ver. 69)

Find the general solution to the given ODE.

\[y'-5y=0\]

Answer.

\[y= k e^{\left(5 \, t\right)}\]

Example 70

C1 - Homogeneous first-order linear ODE (ver. 70)

Find the general solution to the given ODE.

\[y'+9y=0\]

Answer.

\[y= k e^{\left(-9 \, t\right)}\]

Example 71

C1 - Homogeneous first-order linear ODE (ver. 71)

Find the general solution to the given ODE.

\[y'+8y=0\]

Answer.

\[y= k e^{\left(-8 \, t\right)}\]

Example 72

C1 - Homogeneous first-order linear ODE (ver. 72)

Find the general solution to the given ODE.

\[y'-8y=0\]

Answer.

\[y= k e^{\left(8 \, t\right)}\]

Example 73

C1 - Homogeneous first-order linear ODE (ver. 73)

Find the general solution to the given ODE.

\[y'-7y=0\]

Answer.

\[y= k e^{\left(7 \, t\right)}\]

Example 74

C1 - Homogeneous first-order linear ODE (ver. 74)

Find the general solution to the given ODE.

\[y'-3y=0\]

Answer.

\[y= k e^{\left(3 \, t\right)}\]

Example 75

C1 - Homogeneous first-order linear ODE (ver. 75)

Find the general solution to the given ODE.

\[y'+4y=0\]

Answer.

\[y= k e^{\left(-4 \, t\right)}\]

Example 76

C1 - Homogeneous first-order linear ODE (ver. 76)

Find the general solution to the given ODE.

\[y'-9y=0\]

Answer.

\[y= k e^{\left(9 \, t\right)}\]

Example 77

C1 - Homogeneous first-order linear ODE (ver. 77)

Find the general solution to the given ODE.

\[y'-9y=0\]

Answer.

\[y= k e^{\left(9 \, t\right)}\]

Example 78

C1 - Homogeneous first-order linear ODE (ver. 78)

Find the general solution to the given ODE.

\[y'-3y=0\]

Answer.

\[y= k e^{\left(3 \, t\right)}\]

Example 79

C1 - Homogeneous first-order linear ODE (ver. 79)

Find the general solution to the given ODE.

\[y'+3y=0\]

Answer.

\[y= k e^{\left(-3 \, t\right)}\]

Example 80

C1 - Homogeneous first-order linear ODE (ver. 80)

Find the general solution to the given ODE.

\[y'-8y=0\]

Answer.

\[y= k e^{\left(8 \, t\right)}\]

Example 81

C1 - Homogeneous first-order linear ODE (ver. 81)

Find the general solution to the given ODE.

\[y'+8y=0\]

Answer.

\[y= k e^{\left(-8 \, t\right)}\]

Example 82

C1 - Homogeneous first-order linear ODE (ver. 82)

Find the general solution to the given ODE.

\[y'+8y=0\]

Answer.

\[y= k e^{\left(-8 \, t\right)}\]

Example 83

C1 - Homogeneous first-order linear ODE (ver. 83)

Find the general solution to the given ODE.

\[y'+2y=0\]

Answer.

\[y= k e^{\left(-2 \, t\right)}\]

Example 84

C1 - Homogeneous first-order linear ODE (ver. 84)

Find the general solution to the given ODE.

\[y'+7y=0\]

Answer.

\[y= k e^{\left(-7 \, t\right)}\]

Example 85

C1 - Homogeneous first-order linear ODE (ver. 85)

Find the general solution to the given ODE.

\[y'+4y=0\]

Answer.

\[y= k e^{\left(-4 \, t\right)}\]

Example 86

C1 - Homogeneous first-order linear ODE (ver. 86)

Find the general solution to the given ODE.

\[y'+3y=0\]

Answer.

\[y= k e^{\left(-3 \, t\right)}\]

Example 87

C1 - Homogeneous first-order linear ODE (ver. 87)

Find the general solution to the given ODE.

\[y'-5y=0\]

Answer.

\[y= k e^{\left(5 \, t\right)}\]

Example 88

C1 - Homogeneous first-order linear ODE (ver. 88)

Find the general solution to the given ODE.

\[y'+7y=0\]

Answer.

\[y= k e^{\left(-7 \, t\right)}\]

Example 89

C1 - Homogeneous first-order linear ODE (ver. 89)

Find the general solution to the given ODE.

\[y'+8y=0\]

Answer.

\[y= k e^{\left(-8 \, t\right)}\]

Example 90

C1 - Homogeneous first-order linear ODE (ver. 90)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]

Example 91

C1 - Homogeneous first-order linear ODE (ver. 91)

Find the general solution to the given ODE.

\[y'+7y=0\]

Answer.

\[y= k e^{\left(-7 \, t\right)}\]

Example 92

C1 - Homogeneous first-order linear ODE (ver. 92)

Find the general solution to the given ODE.

\[y'-2y=0\]

Answer.

\[y= k e^{\left(2 \, t\right)}\]

Example 93

C1 - Homogeneous first-order linear ODE (ver. 93)

Find the general solution to the given ODE.

\[y'-1y=0\]

Answer.

\[y= k e^{t}\]

Example 94

C1 - Homogeneous first-order linear ODE (ver. 94)

Find the general solution to the given ODE.

\[y'+7y=0\]

Answer.

\[y= k e^{\left(-7 \, t\right)}\]

Example 95

C1 - Homogeneous first-order linear ODE (ver. 95)

Find the general solution to the given ODE.

\[y'-3y=0\]

Answer.

\[y= k e^{\left(3 \, t\right)}\]

Example 96

C1 - Homogeneous first-order linear ODE (ver. 96)

Find the general solution to the given ODE.

\[y'-7y=0\]

Answer.

\[y= k e^{\left(7 \, t\right)}\]

Example 97

C1 - Homogeneous first-order linear ODE (ver. 97)

Find the general solution to the given ODE.

\[y'+2y=0\]

Answer.

\[y= k e^{\left(-2 \, t\right)}\]

Example 98

C1 - Homogeneous first-order linear ODE (ver. 98)

Find the general solution to the given ODE.

\[y'+3y=0\]

Answer.

\[y= k e^{\left(-3 \, t\right)}\]

Example 99

C1 - Homogeneous first-order linear ODE (ver. 99)

Find the general solution to the given ODE.

\[y'+y=0\]

Answer.

\[y= k e^{\left(-t\right)}\]

Example 100

C1 - Homogeneous first-order linear ODE (ver. 100)

Find the general solution to the given ODE.

\[y'-4y=0\]

Answer.

\[y= k e^{\left(4 \, t\right)}\]