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

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

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

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

y = e^{- x} x + c_{1} x

Solution steps

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

Solve linear ODE:

y = e^{- x} x + c_{1} x

y = e^{- x} x + c_{1} x

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