What is the solution for xy^'=xe^{-2x}-(2x+1)y ?

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

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xy^'=xe^{-2x}-(2x+1)y

x y^{^{'}} = x e^{- 2 x} - (2 x + 1) y

y = \frac{x}{2 e ^{2 x}} + \frac{c _{1}}{e ^{2 x} x}

Solution steps

x y^{'} (x) = x e^{- 2 x} - (2 x + 1) y

Solve linear ODE:

y = \frac{x}{2 e ^{2 x}} + \frac{c _{1}}{e ^{2 x} x}

y = \frac{x}{2 e ^{2 x}} + \frac{c _{1}}{e ^{2 x} x}

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