What is the solution for y^{''}-2y^'-63y=-181t+126t^2 ?

The solution for y^{''}-2y^'-63y=-181t+126t^2 is y=c_{1}e^{9t}+c_{2}e^{-7t}-2t^2+3t-10/63

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y^{''}-2y^'-63y=-181t+126t^2

y^{^{''}} - 2 y^{^{'}} - 63 y = - 181 t + 126 t^{2}

y = c_{1} e^{9 t} + c_{2} e^{- 7 t} - 2 t^{2} + 3 t - \frac{10}{63}

Solution steps

y^{''} (t) - 2 y^{'} (t) - 63 y = - 181 t + 126 t^{2}

Solve linear ODE:

y = c_{1} e^{9 t} + c_{2} e^{- 7 t} - 2 t^{2} + 3 t - \frac{10}{63}

y = c_{1} e^{9 t} + c_{2} e^{- 7 t} - 2 t^{2} + 3 t - \frac{10}{63}

What is the solution for y^{''}-2y^'-63y=-181t+126t^2 ?
The solution for y^{''}-2y^'-63y=-181t+126t^2 is y=c_{1}e^{9t}+c_{2}e^{-7t}-2t^2+3t-10/63