What is the solution for (dy)/(dx)=xy^3-xy ?

The solution for (dy)/(dx)=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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(dy)/(dx)=xy^3-xy

\frac{d y}{d x} = 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

\frac{d y}{d 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 \to - 2 lim (9 - x)

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

\int 9 cos (x) d x

\int (x cos (x^{2})) d x

\int (- x^{2} + 4) d x

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