What is the solution for (dy)/(dx)=y(xy^2-1) ?

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

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(dy)/(dx)=y(xy^2-1)

\frac{d y}{d x} = y (x y^{2} - 1)

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

Solution steps

\frac{d y}{d x} = y (x y^{2} - 1)

Solve Bernoulli ODE:

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

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

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