What is the solution for y^'=xy^3-xy ?

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

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y^'=xy^3-xy

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

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

Solution steps

y^{'} (x) = x y^{3} - x y

Solve Bernoulli ODE:

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

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

x^{5} - x^{3} + x, 1

\frac{d y}{d x} = cos (3 x)

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