What is the solution for y^{''}+2y^'-8y=8x^2-3 ?

The solution for y^{''}+2y^'-8y=8x^2-3 is y=c_{1}e^{2x}+c_{2}e^{-4x}-x^2-x/2

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y^{''}+2y^'-8y=8x^2-3

y^{^{''}} + 2 y^{^{'}} - 8 y = 8 x^{2} - 3

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} - x^{2} - \frac{x}{2}

Solution steps

y^{''} (x) + 2 y^{'} (x) - 8 y = 8 x^{2} - 3

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} - x^{2} - \frac{x}{2}

y = c_{1} e^{2 x} + c_{2} e^{- 4 x} - x^{2} - \frac{x}{2}

What is the solution for y^{''}+2y^'-8y=8x^2-3 ?
The solution for y^{''}+2y^'-8y=8x^2-3 is y=c_{1}e^{2x}+c_{2}e^{-4x}-x^2-x/2