What is the solution for y^{''}-5y^'-24y=(t+1)e^t ?

The solution for y^{''}-5y^'-24y=(t+1)e^t is y=c_{1}e^{8t}+c_{2}e^{-3t}-(e^tt)/(28)-25/784 e^t

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y^{''}-5y^'-24y=(t+1)e^t

y^{^{''}} - 5 y^{^{'}} - 24 y = (t + 1) e^{t}

y = c_{1} e^{8 t} + c_{2} e^{- 3 t} - \frac{e ^{t} t}{28} - \frac{25}{784} e^{t}

Solution steps

y^{''} (t) - 5 y^{'} (t) - 24 y = (t + 1) e^{t}

Solve linear ODE:

y = c_{1} e^{8 t} + c_{2} e^{- 3 t} - \frac{e ^{t} t}{28} - \frac{25}{784} e^{t}

y = c_{1} e^{8 t} + c_{2} e^{- 3 t} - \frac{e ^{t} t}{28} - \frac{25}{784} e^{t}

5 y^{^{''}} + y^{^{'}} = - 4 x, y (0) = 0, y^{^{'}} (0) = - 25

\frac{d ^{2} x}{d t ^{2}} + \frac{d x}{d t} = 5 t

3 y^{^{''}} + 2 y^{^{'}} - y = 23

y^{^{''}} - y^{^{'}} - 6 y = 45 cos (3 x)

y^{^{''}} + 4 y^{^{'}} + 3 y = 8 e^{- 2 x}

What is the solution for y^{''}-5y^'-24y=(t+1)e^t ?
The solution for y^{''}-5y^'-24y=(t+1)e^t is y=c_{1}e^{8t}+c_{2}e^{-3t}-(e^tt)/(28)-25/784 e^t