What is the solution for y^{''}+5y^'-36y=-128t+72t^2 ?

The solution for y^{''}+5y^'-36y=-128t+72t^2 is y=c_{1}e^{4t}+c_{2}e^{-9t}-2t^2+3t+11/36

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y^{''}+5y^'-36y=-128t+72t^2

y^{^{''}} + 5 y^{^{'}} - 36 y = - 128 t + 72 t^{2}

y = c_{1} e^{4 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t + \frac{11}{36}

Solution steps

y^{''} (t) + 5 y^{'} (t) - 36 y = - 128 t + 72 t^{2}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t + \frac{11}{36}

y = c_{1} e^{4 t} + c_{2} e^{- 9 t} - 2 t^{2} + 3 t + \frac{11}{36}

y^{^{''}} + 4 y^{^{'}} - 32 y = - 112 t + 64 t^{2}

y^{^{''}} - 36.6 y^{^{'}} + 334.89 y = 18.5 u

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

y^{^{''}} + 3 y^{^{'}} - 4 y = e^{x} + x

x^{^{''}} + 2 x^{^{'}} + 41 x = 12 cos (6 t)

What is the solution for y^{''}+5y^'-36y=-128t+72t^2 ?
The solution for y^{''}+5y^'-36y=-128t+72t^2 is y=c_{1}e^{4t}+c_{2}e^{-9t}-2t^2+3t+11/36