What is the solution for derivative of e^{x^2}y=x ?

The solution for derivative of e^{x^2}y=x is y=(x^2)/(2e^{x^2)}+(c_{1})/(e^{x^2)}

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derivative of e^{x^2}y=x

\frac{d}{d x} (e^{x^{2}} y) = x

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

Solution steps

\frac{d}{d x} (e^{x^{2}} y) = x

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

e^{x^{2}} y = \int x d x

\int x d x = \frac{x ^{2}}{2} + c_{1}

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

Isolate

y : 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 derivative of e^{x^2}y=x ?
The solution for derivative of e^{x^2}y=x is y=(x^2)/(2e^{x^2)}+(c_{1})/(e^{x^2)}