What is the solution for y^{''}-5y^'-24y=5+2t ?

The solution for y^{''}-5y^'-24y=5+2t is y=c_{1}e^{8t}+c_{2}e^{-3t}-t/(12)-55/288

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y^{''}-5y^'-24y=5+2t

y^{^{''}} - 5 y^{^{'}} - 24 y = 5 + 2 t

y = c_{1} e^{8 t} + c_{2} e^{- 3 t} - \frac{t}{12} - \frac{55}{288}

Solution steps

y^{''} (t) - 5 y^{'} (t) - 24 y = 5 + 2 t

Solve linear ODE:

y = c_{1} e^{8 t} + c_{2} e^{- 3 t} - \frac{t}{12} - \frac{55}{288}

y = c_{1} e^{8 t} + c_{2} e^{- 3 t} - \frac{t}{12} - \frac{55}{288}

y^{^{''}} - y^{^{'}} - 2 y = 3 t^{2} - 1

y^{^{''}} + 36 y = 33 cos (5 x)

y^{^{'''}} - y^{^{'}} = 2 \cdot cos (t)

y^{^{''}} + 3 y^{^{'}} + 2 y = cos (2 t)

y^{^{''}} - 3 y^{^{'}} - 6 y = 2 t^{2} + 2 t - 5 e^{3 t}

What is the solution for y^{''}-5y^'-24y=5+2t ?
The solution for y^{''}-5y^'-24y=5+2t is y=c_{1}e^{8t}+c_{2}e^{-3t}-t/(12)-55/288