What is the solution for (d^2y)/(dx^2)-y=x*e^x ?

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

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(d^2y)/(dx^2)-y=x*e^x

\frac{d ^{2} y}{d x ^{2}} - y = x \cdot e^{x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - y = x \cdot e^{x}

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 13 e^{3 x}

y^{^{''}} - y = e^{t} sin (t), y (0) = 0, y^{^{'}} (0) = 0

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

y^{^{''}} + 4 y = x cos (2 x)

y^{^{''}} + y = sin (x) + x cos (x)

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