What is the solution for e^{x^2}(dy)/(dx)+2e^{x^2}xy=e^{x^2}x ?

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

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e^{x^2}(dy)/(dx)+2e^{x^2}xy=e^{x^2}x

e^{x^{2}} \frac{d y}{d x} + 2 e^{x^{2}} x y = e^{x^{2}} x

y = \frac{e ^{- x^{2} - c_{1}}}{2} + \frac{1}{2}

Solution steps

e^{x^{2}} \frac{d y}{d x} + 2 e^{x^{2}} x y = e^{x^{2}} x

Solve separable ODE:

y = \frac{e ^{- x^{2} - c_{1}}}{2} + \frac{1}{2}

y = \frac{e ^{- x^{2} - c_{1}}}{2} + \frac{1}{2}

d y = \frac{8 y}{x} d x

y^{^{'}} = \frac{y - 1}{x + 1}

y d x - x d y = 2 d y, y (1) = 1

\frac{d y}{d t} = y + 4

\frac{d y}{d t} - 6 t^{2} e^{- y} = 0

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