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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = - 2 \cdot t \cdot y^{2}, y (0) = 1

x^{\frac{1}{3}} y^{^{'}} + y = 0

y^{^{'}} = x y^{3} \cdot (1 + x^{2})^{(\frac{- 1}{2})}

3 y^{2} d y - t d t = 0

y^{^{'}} - 3 y = - 6 y^{2}

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