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

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

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

y^{^{'}} + 2 x y = x e^{- x^{2}}

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

Solution steps

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

Solve linear ODE:

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

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

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