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

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

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x*(dy)/(dx)+y=e^{-x}

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

y = - \frac{e ^{- x}}{x} + \frac{c _{1}}{x}

Solution steps

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

Solve linear ODE:

y = - \frac{e ^{- x}}{x} + \frac{c _{1}}{x}

y = - \frac{e ^{- x}}{x} + \frac{c _{1}}{x}

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