What is the solution for y^{''}-6y^'-16y=-24t+32t^2 ?

The solution for y^{''}-6y^'-16y=-24t+32t^2 is y=c_{1}e^{8t}+c_{2}e^{-2t}-2t^2+3t-11/8

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y^{''}-6y^'-16y=-24t+32t^2

y^{^{''}} - 6 y^{^{'}} - 16 y = - 24 t + 32 t^{2}

y = c_{1} e^{8 t} + c_{2} e^{- 2 t} - 2 t^{2} + 3 t - \frac{11}{8}

Solution steps

y^{''} (t) - 6 y^{'} (t) - 16 y = - 24 t + 32 t^{2}

Solve linear ODE:

y = c_{1} e^{8 t} + c_{2} e^{- 2 t} - 2 t^{2} + 3 t - \frac{11}{8}

y = c_{1} e^{8 t} + c_{2} e^{- 2 t} - 2 t^{2} + 3 t - \frac{11}{8}

What is the solution for y^{''}-6y^'-16y=-24t+32t^2 ?
The solution for y^{''}-6y^'-16y=-24t+32t^2 is y=c_{1}e^{8t}+c_{2}e^{-2t}-2t^2+3t-11/8