What is the solution for y^'+xy= x/(y^3) ?

The solution for y^'+xy= x/(y^3) is y=\sqrt[4]{-e^{-2x^2-c_{1}}+1},y=-\sqrt[4]{-e^{-2x^2-c_{1}}+1}

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y^'+xy= x/(y^3)

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

y = 4 - e^{- 2 x^{2} - c_{1}} + 1, y = - 4 - e^{- 2 x^{2} - c_{1}} + 1

Solution steps

y^{'} (x) + x y = \frac{x}{y ^{3}}

Solve separable ODE:

y = 4 - e^{- 2 x^{2} - c_{1}} + 1, y = - 4 - e^{- 2 x^{2} - c_{1}} + 1

y = 4 - e^{- 2 x^{2} - c_{1}} + 1, y = - 4 - e^{- 2 x^{2} - c_{1}} + 1

y - y^{2} + x y^{^{'}} = 0

e^{x} \frac{d y}{d x} + y^{3} = x y^{3}

y^{^{'}} = a y

\frac{d y}{d x} = x^{3} y^{4}

y^{^{'}} = \frac{1}{2} x 1 - 16 y^{2}

What is the solution for y^'+xy= x/(y^3) ?
The solution for y^'+xy= x/(y^3) is y=\sqrt[4]{-e^{-2x^2-c_{1}}+1},y=-\sqrt[4]{-e^{-2x^2-c_{1}}+1}