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

The solution for y^{''}-y=xe^{2x} is y=c_{1}e^x+c_{2}e^{-x}+(e^{2x}x)/3-4/9 e^{2x}

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

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

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for y^{''}-y=xe^{2x} ?
The solution for y^{''}-y=xe^{2x} is y=c_{1}e^x+c_{2}e^{-x}+(e^{2x}x)/3-4/9 e^{2x}