What is the solution for y^'+ky=e^{-kx} ?

The solution for y^'+ky=e^{-kx} is y= x/(e^{kx)}+(c_{1})/(e^{kx)}

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y^'+ky=e^{-kx}

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

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for y^'+ky=e^{-kx} ?
The solution for y^'+ky=e^{-kx} is y= x/(e^{kx)}+(c_{1})/(e^{kx)}