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

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

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

y^{^{'}} + 2 x y = x \cdot 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 \cdot 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}}}

\frac{\partial}{\partial x} (2 ln ((x + y)^{3}))

\frac{d}{d x} ((14 x - x^{2})^{3})

f (x) = 8 x^{2} + 8 x - 5, at x = - \frac{1}{2}

\frac{d}{d x} (\frac{4 x}{5 - tan ( x )})

\int - \frac{x ^{2}}{2 ( x + 1 )} d x

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