What is the solution for derivative of (y^2)=y^2x ?

The solution for derivative of (y^2)=y^2x is y=e^{(x^2)/4+c_{1}}

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derivative of (y^2)=y^2x

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

y = e^{\frac{x ^{2}}{4} + c_{1}}

Solution steps

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

Solve separable ODE:

y = e^{\frac{x ^{2}}{4} + c_{1}}

y = e^{\frac{x ^{2}}{4} + c_{1}}

\frac{d y}{d x} = \frac{x ^{3} + 1}{y}, y = 2, x = 1

\frac{d y}{d x} y - 6 x^{3} + cos (x) = 0

y^{^{'}} = 3 y - 15

y^{^{'}} = \frac{x y ^{3}}{5}, y (0) = 5

\frac{d x}{d y} = \frac{4}{x e ^{y}}

What is the solution for derivative of (y^2)=y^2x ?
The solution for derivative of (y^2)=y^2x is y=e^{(x^2)/4+c_{1}}