What is the solution for (dy)/(dx)-y=xe^x ?

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

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(dy)/(dx)-y=xe^x

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

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

Solution steps

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

Solve linear ODE:

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

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

x \to 3 lim (3 x^{2} - 7 x + 2)

x \to 5 + lim (- \frac{x}{x - 5})

\int \frac{1}{y ^{2} - 2 y} d y

3 y^{^{'}} + y = 0, y (0) = 0

n \to \infty lim (\frac{1}{e})

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