What is the solution for y^{''}-4y=x^2 ?

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

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y^{''}-4y=x^2

y^{^{''}} - 4 y = x^{2}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} - \frac{1}{8}

Solution steps

y^{''} (x) - 4 y = x^{2}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} - \frac{1}{8}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{4} - \frac{1}{8}

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