C2 - Non-homogeneous first-order linear ODE (ver. 1)

Find the general solution to the given ODE.

$y'-5y= -9 \, \cos\left(-3 \, t\right) e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} + 3 \, e^{\left(5 \, t\right)} \sin\left(-3 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 2)

Find the general solution to the given ODE.

$y'+5y= 2 \, \cos\left(-t\right) e^{\left(-5 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 2 \, e^{\left(-5 \, t\right)} \sin\left(-t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 3)

Find the general solution to the given ODE.

$y'-3y= 15 \, e^{\left(3 \, t\right)} \sin\left(-5 \, t\right)$

$y= k e^{\left(3 \, t\right)} + 3 \, \cos\left(-5 \, t\right) e^{\left(3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 4)

Find the general solution to the given ODE.

$y'+4y= 15 \, e^{t}$

$y= k e^{\left(-4 \, t\right)} + 3 \, e^{t}$

C2 - Non-homogeneous first-order linear ODE (ver. 5)

Find the general solution to the given ODE.

$y'-1y= 2 \, e^{t}$

$y= k e^{t} + 2 \, t e^{t}$

C2 - Non-homogeneous first-order linear ODE (ver. 6)

Find the general solution to the given ODE.

$y'-5y= 2 \, e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} + 2 \, t e^{\left(5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 7)

Find the general solution to the given ODE.

$y'-5y= 9 \, \cos\left(3 \, t\right) e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} + 3 \, e^{\left(5 \, t\right)} \sin\left(3 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 8)

Find the general solution to the given ODE.

$y'-5y= 9 \, e^{\left(5 \, t\right)} \sin\left(-3 \, t\right)$

$y= k e^{\left(5 \, t\right)} + 3 \, \cos\left(-3 \, t\right) e^{\left(5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 9)

Find the general solution to the given ODE.

$y'+4y= -3 \, e^{\left(-4 \, t\right)}$

$y= k e^{\left(-4 \, t\right)} - 3 \, t e^{\left(-4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 10)

Find the general solution to the given ODE.

$y'+5y= 6 \, e^{\left(-3 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} + 3 \, e^{\left(-3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 11)

Find the general solution to the given ODE.

$y'+3y= -4 \, e^{\left(-t\right)}$

$y= k e^{\left(-3 \, t\right)} - 2 \, e^{\left(-t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 12)

Find the general solution to the given ODE.

$y'-3y= -4 \, e^{\left(3 \, t\right)} \sin\left(2 \, t\right)$

$y= k e^{\left(3 \, t\right)} + 2 \, \cos\left(2 \, t\right) e^{\left(3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 13)

Find the general solution to the given ODE.

$y'-2y= -3 \, e^{\left(2 \, t\right)}$

$y= k e^{\left(2 \, t\right)} - 3 \, t e^{\left(2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 14)

Find the general solution to the given ODE.

$y'+y= 10 \, \cos\left(-5 \, t\right) e^{\left(-t\right)}$

$y= k e^{\left(-t\right)} - 2 \, e^{\left(-t\right)} \sin\left(-5 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 15)

Find the general solution to the given ODE.

$y'-4y= -6 \, e^{t}$

$y= k e^{\left(4 \, t\right)} + 2 \, e^{t}$

C2 - Non-homogeneous first-order linear ODE (ver. 16)

Find the general solution to the given ODE.

$y'-3y= 3 \, e^{\left(3 \, t\right)} \sin\left(t\right)$

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

C2 - Non-homogeneous first-order linear ODE (ver. 17)

Find the general solution to the given ODE.

$y'+3y= -6 \, \cos\left(3 \, t\right) e^{\left(-3 \, t\right)}$

$y= k e^{\left(-3 \, t\right)} - 2 \, e^{\left(-3 \, t\right)} \sin\left(3 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 18)

Find the general solution to the given ODE.

$y'+5y= 3 \, e^{\left(-5 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} + 3 \, t e^{\left(-5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 19)

Find the general solution to the given ODE.

$y'-2y= -2 \, e^{\left(2 \, t\right)}$

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

C2 - Non-homogeneous first-order linear ODE (ver. 20)

Find the general solution to the given ODE.

$y'-3y= -15 \, e^{\left(3 \, t\right)} \sin\left(-5 \, t\right)$

$y= k e^{\left(3 \, t\right)} - 3 \, \cos\left(-5 \, t\right) e^{\left(3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 21)

Find the general solution to the given ODE.

$y'+2y= 3 \, e^{\left(-2 \, t\right)}$

$y= k e^{\left(-2 \, t\right)} + 3 \, t e^{\left(-2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 22)

Find the general solution to the given ODE.

$y'+2y= 3 \, e^{\left(-2 \, t\right)} \sin\left(-t\right)$

$y= k e^{\left(-2 \, t\right)} + 3 \, \cos\left(-t\right) e^{\left(-2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 23)

Find the general solution to the given ODE.

$y'+y= -8 \, e^{\left(-5 \, t\right)}$

$y= k e^{\left(-t\right)} + 2 \, e^{\left(-5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 24)

Find the general solution to the given ODE.

$y'-3y= 3 \, e^{\left(3 \, t\right)}$

$y= k e^{\left(3 \, t\right)} + 3 \, t e^{\left(3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 25)

Find the general solution to the given ODE.

$y'-3y= 10 \, e^{\left(3 \, t\right)} \sin\left(5 \, t\right)$

$y= k e^{\left(3 \, t\right)} - 2 \, \cos\left(5 \, t\right) e^{\left(3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 26)

Find the general solution to the given ODE.

$y'-5y= -2 \, e^{\left(5 \, t\right)} \sin\left(t\right)$

$y= k e^{\left(5 \, t\right)} + 2 \, \cos\left(t\right) e^{\left(5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 27)

Find the general solution to the given ODE.

$y'-1y= 15 \, \cos\left(-5 \, t\right) e^{t}$

$y= k e^{t} - 3 \, e^{t} \sin\left(-5 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 28)

Find the general solution to the given ODE.

$y'-3y= -15 \, e^{\left(3 \, t\right)} \sin\left(-5 \, t\right)$

$y= k e^{\left(3 \, t\right)} - 3 \, \cos\left(-5 \, t\right) e^{\left(3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 29)

Find the general solution to the given ODE.

$y'-5y= -4 \, \cos\left(-2 \, t\right) e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} + 2 \, e^{\left(5 \, t\right)} \sin\left(-2 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 30)

Find the general solution to the given ODE.

$y'-2y= -2 \, e^{t}$

$y= k e^{\left(2 \, t\right)} + 2 \, e^{t}$

C2 - Non-homogeneous first-order linear ODE (ver. 31)

Find the general solution to the given ODE.

$y'-1y= 3 \, e^{t}$

$y= k e^{t} + 3 \, t e^{t}$

C2 - Non-homogeneous first-order linear ODE (ver. 32)

Find the general solution to the given ODE.

$y'-3y= 8 \, e^{\left(3 \, t\right)} \sin\left(4 \, t\right)$

$y= k e^{\left(3 \, t\right)} - 2 \, \cos\left(4 \, t\right) e^{\left(3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 33)

Find the general solution to the given ODE.

$y'+y= -15 \, \cos\left(5 \, t\right) e^{\left(-t\right)}$

$y= k e^{\left(-t\right)} - 3 \, e^{\left(-t\right)} \sin\left(5 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 34)

Find the general solution to the given ODE.

$y'-4y= 6 \, e^{\left(4 \, t\right)} \sin\left(-2 \, t\right)$

$y= k e^{\left(4 \, t\right)} + 3 \, \cos\left(-2 \, t\right) e^{\left(4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 35)

Find the general solution to the given ODE.

$y'-2y= -6 \, e^{\left(2 \, t\right)} \sin\left(3 \, t\right)$

$y= k e^{\left(2 \, t\right)} + 2 \, \cos\left(3 \, t\right) e^{\left(2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 36)

Find the general solution to the given ODE.

$y'+5y= -4 \, e^{\left(-3 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 2 \, e^{\left(-3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 37)

Find the general solution to the given ODE.

$y'-4y= 10 \, \cos\left(-5 \, t\right) e^{\left(4 \, t\right)}$

$y= k e^{\left(4 \, t\right)} - 2 \, e^{\left(4 \, t\right)} \sin\left(-5 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 38)

Find the general solution to the given ODE.

$y'+2y= 3 \, e^{\left(-2 \, t\right)} \sin\left(t\right)$

$y= k e^{\left(-2 \, t\right)} - 3 \, \cos\left(t\right) e^{\left(-2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 39)

Find the general solution to the given ODE.

$y'+5y= -3 \, e^{\left(-4 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 3 \, e^{\left(-4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 40)

Find the general solution to the given ODE.

$y'+2y= -2 \, \cos\left(-t\right) e^{\left(-2 \, t\right)}$

$y= k e^{\left(-2 \, t\right)} + 2 \, e^{\left(-2 \, t\right)} \sin\left(-t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 41)

Find the general solution to the given ODE.

$y'-2y= -10 \, e^{\left(2 \, t\right)} \sin\left(-5 \, t\right)$

$y= k e^{\left(2 \, t\right)} - 2 \, \cos\left(-5 \, t\right) e^{\left(2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 42)

Find the general solution to the given ODE.

$y'-2y= -2 \, e^{\left(2 \, t\right)}$

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

C2 - Non-homogeneous first-order linear ODE (ver. 43)

Find the general solution to the given ODE.

$y'-2y= -6 \, e^{\left(2 \, t\right)} \sin\left(3 \, t\right)$

$y= k e^{\left(2 \, t\right)} + 2 \, \cos\left(3 \, t\right) e^{\left(2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 44)

Find the general solution to the given ODE.

$y'+y= -6 \, e^{\left(-3 \, t\right)}$

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

C2 - Non-homogeneous first-order linear ODE (ver. 45)

Find the general solution to the given ODE.

$y'-5y= -3 \, e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} - 3 \, t e^{\left(5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 46)

Find the general solution to the given ODE.

$y'-2y= -15 \, e^{\left(-3 \, t\right)}$

$y= k e^{\left(2 \, t\right)} + 3 \, e^{\left(-3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 47)

Find the general solution to the given ODE.

$y'+5y= -3 \, e^{\left(-5 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 3 \, t e^{\left(-5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 48)

Find the general solution to the given ODE.

$y'-1y= 8 \, \cos\left(4 \, t\right) e^{t}$

$y= k e^{t} + 2 \, e^{t} \sin\left(4 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 49)

Find the general solution to the given ODE.

$y'+3y= -6 \, e^{\left(-3 \, t\right)} \sin\left(-2 \, t\right)$

$y= k e^{\left(-3 \, t\right)} - 3 \, \cos\left(-2 \, t\right) e^{\left(-3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 50)

Find the general solution to the given ODE.

$y'+3y= -2 \, e^{\left(-3 \, t\right)}$

$y= k e^{\left(-3 \, t\right)} - 2 \, t e^{\left(-3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 51)

Find the general solution to the given ODE.

$y'+2y= -12 \, e^{\left(-2 \, t\right)} \sin\left(4 \, t\right)$

$y= k e^{\left(-2 \, t\right)} + 3 \, \cos\left(4 \, t\right) e^{\left(-2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 52)

Find the general solution to the given ODE.

$y'-2y= 6 \, \cos\left(3 \, t\right) e^{\left(2 \, t\right)}$

$y= k e^{\left(2 \, t\right)} + 2 \, e^{\left(2 \, t\right)} \sin\left(3 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 53)

Find the general solution to the given ODE.

$y'-4y= -18 \, e^{\left(-5 \, t\right)}$

$y= k e^{\left(4 \, t\right)} + 2 \, e^{\left(-5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 54)

Find the general solution to the given ODE.

$y'-4y= -3 \, e^{\left(3 \, t\right)}$

$y= k e^{\left(4 \, t\right)} + 3 \, e^{\left(3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 55)

Find the general solution to the given ODE.

$y'-5y= 2 \, e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} + 2 \, t e^{\left(5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 56)

Find the general solution to the given ODE.

$y'+3y= 8 \, e^{\left(-3 \, t\right)} \sin\left(4 \, t\right)$

$y= k e^{\left(-3 \, t\right)} - 2 \, \cos\left(4 \, t\right) e^{\left(-3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 57)

Find the general solution to the given ODE.

$y'+4y= 8 \, \cos\left(4 \, t\right) e^{\left(-4 \, t\right)}$

$y= k e^{\left(-4 \, t\right)} + 2 \, e^{\left(-4 \, t\right)} \sin\left(4 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 58)

Find the general solution to the given ODE.

$y'+4y= -4 \, e^{\left(-2 \, t\right)}$

$y= k e^{\left(-4 \, t\right)} - 2 \, e^{\left(-2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 59)

Find the general solution to the given ODE.

$y'+2y= 3 \, e^{\left(-2 \, t\right)}$

$y= k e^{\left(-2 \, t\right)} + 3 \, t e^{\left(-2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 60)

Find the general solution to the given ODE.

$y'+2y= 2 \, e^{\left(-2 \, t\right)} \sin\left(-t\right)$

$y= k e^{\left(-2 \, t\right)} + 2 \, \cos\left(-t\right) e^{\left(-2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 61)

Find the general solution to the given ODE.

$y'-1y= 4 \, \cos\left(2 \, t\right) e^{t}$

$y= k e^{t} + 2 \, e^{t} \sin\left(2 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 62)

Find the general solution to the given ODE.

$y'+y= -2 \, e^{\left(-t\right)}$

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

C2 - Non-homogeneous first-order linear ODE (ver. 63)

Find the general solution to the given ODE.

$y'+5y= -2 \, e^{\left(-5 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 2 \, t e^{\left(-5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 64)

Find the general solution to the given ODE.

$y'-5y= -2 \, \cos\left(t\right) e^{\left(5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} - 2 \, e^{\left(5 \, t\right)} \sin\left(t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 65)

Find the general solution to the given ODE.

$y'+4y= 9 \, e^{\left(-4 \, t\right)} \sin\left(-3 \, t\right)$

$y= k e^{\left(-4 \, t\right)} + 3 \, \cos\left(-3 \, t\right) e^{\left(-4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 66)

Find the general solution to the given ODE.

$y'+3y= -3 \, e^{\left(-3 \, t\right)}$

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

C2 - Non-homogeneous first-order linear ODE (ver. 67)

Find the general solution to the given ODE.

$y'-5y= -30 \, e^{\left(-5 \, t\right)}$

$y= k e^{\left(5 \, t\right)} + 3 \, e^{\left(-5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 68)

Find the general solution to the given ODE.

$y'-1y= 15 \, e^{t} \sin\left(5 \, t\right)$

$y= k e^{t} - 3 \, \cos\left(5 \, t\right) e^{t}$

C2 - Non-homogeneous first-order linear ODE (ver. 69)

Find the general solution to the given ODE.

$y'-3y= -12 \, e^{\left(-3 \, t\right)}$

$y= k e^{\left(3 \, t\right)} + 2 \, e^{\left(-3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 70)

Find the general solution to the given ODE.

$y'+5y= -3 \, \cos\left(t\right) e^{\left(-5 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 3 \, e^{\left(-5 \, t\right)} \sin\left(t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 71)

Find the general solution to the given ODE.

$y'+5y= -4 \, \cos\left(-2 \, t\right) e^{\left(-5 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} + 2 \, e^{\left(-5 \, t\right)} \sin\left(-2 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 72)

Find the general solution to the given ODE.

$y'-4y= -2 \, e^{\left(4 \, t\right)}$

$y= k e^{\left(4 \, t\right)} - 2 \, t e^{\left(4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 73)

Find the general solution to the given ODE.

$y'-4y= 6 \, e^{\left(4 \, t\right)} \sin\left(3 \, t\right)$

$y= k e^{\left(4 \, t\right)} - 2 \, \cos\left(3 \, t\right) e^{\left(4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 74)

Find the general solution to the given ODE.

$y'-2y= 3 \, e^{\left(2 \, t\right)}$

$y= k e^{\left(2 \, t\right)} + 3 \, t e^{\left(2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 75)

Find the general solution to the given ODE.

$y'+2y= -15 \, \cos\left(-5 \, t\right) e^{\left(-2 \, t\right)}$

$y= k e^{\left(-2 \, t\right)} + 3 \, e^{\left(-2 \, t\right)} \sin\left(-5 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 76)

Find the general solution to the given ODE.

$y'-5y= 8 \, e^{\left(5 \, t\right)} \sin\left(4 \, t\right)$

$y= k e^{\left(5 \, t\right)} - 2 \, \cos\left(4 \, t\right) e^{\left(5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 77)

Find the general solution to the given ODE.

$y'-5y= 18 \, e^{\left(-4 \, t\right)}$

$y= k e^{\left(5 \, t\right)} - 2 \, e^{\left(-4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 78)

Find the general solution to the given ODE.

$y'-2y= 18 \, e^{\left(-4 \, t\right)}$

$y= k e^{\left(2 \, t\right)} - 3 \, e^{\left(-4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 79)

Find the general solution to the given ODE.

$y'+2y= 6 \, e^{\left(-4 \, t\right)}$

$y= k e^{\left(-2 \, t\right)} - 3 \, e^{\left(-4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 80)

Find the general solution to the given ODE.

$y'-4y= -2 \, e^{\left(4 \, t\right)} \sin\left(-t\right)$

$y= k e^{\left(4 \, t\right)} - 2 \, \cos\left(-t\right) e^{\left(4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 81)

Find the general solution to the given ODE.

$y'+5y= -3 \, e^{\left(-4 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 3 \, e^{\left(-4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 82)

Find the general solution to the given ODE.

$y'+5y= 4 \, e^{\left(-5 \, t\right)} \sin\left(-2 \, t\right)$

$y= k e^{\left(-5 \, t\right)} + 2 \, \cos\left(-2 \, t\right) e^{\left(-5 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 83)

Find the general solution to the given ODE.

$y'+y= 6 \, e^{\left(-3 \, t\right)}$

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

C2 - Non-homogeneous first-order linear ODE (ver. 84)

Find the general solution to the given ODE.

$y'+4y= -2 \, e^{\left(-4 \, t\right)}$

$y= k e^{\left(-4 \, t\right)} - 2 \, t e^{\left(-4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 85)

Find the general solution to the given ODE.

$y'+2y= 8 \, e^{\left(-2 \, t\right)} \sin\left(-4 \, t\right)$

$y= k e^{\left(-2 \, t\right)} + 2 \, \cos\left(-4 \, t\right) e^{\left(-2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 86)

Find the general solution to the given ODE.

$y'+2y= -6 \, e^{\left(-2 \, t\right)} \sin\left(2 \, t\right)$

$y= k e^{\left(-2 \, t\right)} + 3 \, \cos\left(2 \, t\right) e^{\left(-2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 87)

Find the general solution to the given ODE.

$y'-3y= 3 \, e^{\left(4 \, t\right)}$

$y= k e^{\left(3 \, t\right)} + 3 \, e^{\left(4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 88)

Find the general solution to the given ODE.

$y'+4y= -4 \, e^{\left(-4 \, t\right)} \sin\left(2 \, t\right)$

$y= k e^{\left(-4 \, t\right)} + 2 \, \cos\left(2 \, t\right) e^{\left(-4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 89)

Find the general solution to the given ODE.

$y'+5y= -12 \, \cos\left(4 \, t\right) e^{\left(-5 \, t\right)}$

$y= k e^{\left(-5 \, t\right)} - 3 \, e^{\left(-5 \, t\right)} \sin\left(4 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 90)

Find the general solution to the given ODE.

$y'-3y= -2 \, e^{\left(3 \, t\right)}$

$y= k e^{\left(3 \, t\right)} - 2 \, t e^{\left(3 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 91)

Find the general solution to the given ODE.

$y'+4y= 15 \, \cos\left(5 \, t\right) e^{\left(-4 \, t\right)}$

$y= k e^{\left(-4 \, t\right)} + 3 \, e^{\left(-4 \, t\right)} \sin\left(5 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 92)

Find the general solution to the given ODE.

$y'-1y= -3 \, \cos\left(-t\right) e^{t}$

$y= k e^{t} + 3 \, e^{t} \sin\left(-t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 93)

Find the general solution to the given ODE.

$y'-1y= -12 \, e^{t} \sin\left(-4 \, t\right)$

$y= k e^{t} - 3 \, \cos\left(-4 \, t\right) e^{t}$

C2 - Non-homogeneous first-order linear ODE (ver. 94)

Find the general solution to the given ODE.

$y'+4y= -9 \, \cos\left(3 \, t\right) e^{\left(-4 \, t\right)}$

$y= k e^{\left(-4 \, t\right)} - 3 \, e^{\left(-4 \, t\right)} \sin\left(3 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 95)

Find the general solution to the given ODE.

$y'-2y= 2 \, e^{\left(2 \, t\right)}$

$y= k e^{\left(2 \, t\right)} + 2 \, t e^{\left(2 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 96)

Find the general solution to the given ODE.

$y'-4y= 9 \, e^{\left(4 \, t\right)} \sin\left(3 \, t\right)$

$y= k e^{\left(4 \, t\right)} - 3 \, \cos\left(3 \, t\right) e^{\left(4 \, t\right)}$

C2 - Non-homogeneous first-order linear ODE (ver. 97)

Find the general solution to the given ODE.

$y'+y= 10 \, \cos\left(5 \, t\right) e^{\left(-t\right)}$

$y= k e^{\left(-t\right)} + 2 \, e^{\left(-t\right)} \sin\left(5 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 98)

Find the general solution to the given ODE.

$y'+2y= -8 \, \cos\left(-4 \, t\right) e^{\left(-2 \, t\right)}$

$y= k e^{\left(-2 \, t\right)} + 2 \, e^{\left(-2 \, t\right)} \sin\left(-4 \, t\right)$

C2 - Non-homogeneous first-order linear ODE (ver. 99)

Find the general solution to the given ODE.

$y'+y= 3 \, e^{\left(-t\right)}$

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

C2 - Non-homogeneous first-order linear ODE (ver. 100)

Find the general solution to the given ODE.

$y'-2y= -3 \, e^{\left(2 \, t\right)}$

$y= k e^{\left(2 \, t\right)} - 3 \, t e^{\left(2 \, t\right)}$