What is the solution for y^{''}-2y^'-15y=-37t+30t^2 ?

The solution for y^{''}-2y^'-15y=-37t+30t^2 is y=c_{1}e^{5t}+c_{2}e^{-3t}-2t^2+3t-2/3

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y^{''}-2y^'-15y=-37t+30t^2

y^{^{''}} - 2 y^{^{'}} - 15 y = - 37 t + 30 t^{2}

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

Solution steps

y^{''} (t) - 2 y^{'} (t) - 15 y = - 37 t + 30 t^{2}

Solve linear ODE:

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

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

What is the solution for y^{''}-2y^'-15y=-37t+30t^2 ?
The solution for y^{''}-2y^'-15y=-37t+30t^2 is y=c_{1}e^{5t}+c_{2}e^{-3t}-2t^2+3t-2/3