Решите уравнение y'+2y=e^-x

Решите задачу:

$y'+2y=e^{-x}\\y=uv;y'=u'v+v'u\\u'v+v'u+2uv=e^{-x}\\u'v+u(2v+v')=e^{-x}\\\begin{cases}2v+v'=0\\u'v=e^{-x}\end{cases}\\2v+\frac{dv}{dx}=0|*\frac{dx}{v}\\2dx+\frac{dv}{v}=0\\\frac{dv}{v}=-2dx\\\int\frac{dv}{v}=-2\int dx\\ln|v|=-2x\\v=e^{-2x}\\\frac{du}{dx}*e^{-2x}=e^{-x}|*\frac{dx}{e^{-2x}}\\du=e^{x}dx\\\int du=\int e^xdx\\u=e^x+C\\y=e^{-2x}(e^x+C)$