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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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