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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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