What is the solution for 2y^{''}-y^'-y=5xe^{2x} ?

The solution for 2y^{''}-y^'-y=5xe^{2x} is y=c_{1}e^x+c_{2}e^{-x/2}+e^{2x}x-7/5 e^{2x}

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2y^{''}-y^'-y=5xe^{2x}

2 y^{^{''}} - y^{^{'}} - y = 5 x e^{2 x}

y = c_{1} e^{x} + c_{2} e^{- \frac{x}{2}} + e^{2 x} x - \frac{7}{5} e^{2 x}

Solution steps

2 y^{''} (x) - y^{'} (x) - y = 5 x e^{2 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- \frac{x}{2}} + e^{2 x} x - \frac{7}{5} e^{2 x}

y = c_{1} e^{x} + c_{2} e^{- \frac{x}{2}} + e^{2 x} x - \frac{7}{5} e^{2 x}

What is the solution for 2y^{''}-y^'-y=5xe^{2x} ?
The solution for 2y^{''}-y^'-y=5xe^{2x} is y=c_{1}e^x+c_{2}e^{-x/2}+e^{2x}x-7/5 e^{2x}