What is the solution for y^{''}-2y^'-48y=-136t+96t^2 ?

The solution for y^{''}-2y^'-48y=-136t+96t^2 is y=c_{1}e^{8t}+c_{2}e^{-6t}-2t^2+3t-5/24

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y^{''}-2y^'-48y=-136t+96t^2

y^{^{''}} - 2 y^{^{'}} - 48 y = - 136 t + 96 t^{2}

y = c_{1} e^{8 t} + c_{2} e^{- 6 t} - 2 t^{2} + 3 t - \frac{5}{24}

Solution steps

y^{''} (t) - 2 y^{'} (t) - 48 y = - 136 t + 96 t^{2}

Solve linear ODE:

y = c_{1} e^{8 t} + c_{2} e^{- 6 t} - 2 t^{2} + 3 t - \frac{5}{24}

y = c_{1} e^{8 t} + c_{2} e^{- 6 t} - 2 t^{2} + 3 t - \frac{5}{24}

y^{^{''}} + 15 y^{^{'}} + 56 y = e^{- 6 x}

y^{^{''}} + 4 y = 6 cos (2 x)

y^{^{''}} + 3 y^{^{'}} - 10 y = e^{2 x} + x e^{- 5 x}

y^{^{'''}} - y^{^{''}} - 25 y^{^{'}} + 25 y = 6 - e^{x} + e^{5 x}

y^{^{''''}} + 2 y^{^{''}} + y = 7 + cos (3 t)

What is the solution for y^{''}-2y^'-48y=-136t+96t^2 ?
The solution for y^{''}-2y^'-48y=-136t+96t^2 is y=c_{1}e^{8t}+c_{2}e^{-6t}-2t^2+3t-5/24