What is the solution for y^{''}-64y=-192t+128t^2 ?

The solution for y^{''}-64y=-192t+128t^2 is y=c_{1}e^{8t}+c_{2}e^{-8t}-2t^2+3t-1/16

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y^{''}-64y=-192t+128t^2

y^{^{''}} - 64 y = - 192 t + 128 t^{2}

y = c_{1} e^{8 t} + c_{2} e^{- 8 t} - 2 t^{2} + 3 t - \frac{1}{16}

Solution steps

y^{''} (t) - 64 y = - 192 t + 128 t^{2}

Solve linear ODE:

y = c_{1} e^{8 t} + c_{2} e^{- 8 t} - 2 t^{2} + 3 t - \frac{1}{16}

y = c_{1} e^{8 t} + c_{2} e^{- 8 t} - 2 t^{2} + 3 t - \frac{1}{16}

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 2 x + 3 e^{2 x}

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

y^{^{''}} + 2 y^{^{'}} - 3 y = 32 (3 x + 1) e^{- 3 x}

y^{^{''}} + y^{^{'}} = cos (2 t), y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 2 y^{^{'}} + 1 = e^{x}

What is the solution for y^{''}-64y=-192t+128t^2 ?
The solution for y^{''}-64y=-192t+128t^2 is y=c_{1}e^{8t}+c_{2}e^{-8t}-2t^2+3t-1/16