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

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

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xy^'-y=y^3

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

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

Solution steps

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

Solve Bernoulli ODE:

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

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

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