What is the solution for x^3(dy)/(dx)=x^2y-y^3 ?

The solution for x^3(dy)/(dx)=x^2y-y^3 is y= x/(sqrt(2ln(x)+c_{1))},y=-x/(sqrt(2ln(x)+c_{1))}

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x^3(dy)/(dx)=x^2y-y^3

x^{3} \frac{d y}{d x} = x^{2} y - y^{3}

y = \frac{x}{2 ln ( x ) + c _{1}}, y = - \frac{x}{2 ln ( x ) + c _{1}}

Solution steps

x^{3} \frac{d y}{d x} = x^{2} y - y^{3}

Solve Bernoulli ODE:

y = \frac{x}{2 ln ( x ) + c _{1}}, y = - \frac{x}{2 ln ( x ) + c _{1}}

y = \frac{x}{2 ln ( x ) + c _{1}}, y = - \frac{x}{2 ln ( x ) + c _{1}}

5 x^{\frac{1}{3}} - 5 x^{- \frac{2}{3}}

\frac{d}{d x} (lo g_{2} (7 - 3 x))

x \to 0 + lim ((tan (8 x))^{x})

(x^{2} + 1)^{x}

\frac{16}{s ( s ^{2} + 4 s + 16 )}

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