What is the solution for x^3(dy)/(dx)-x^2y-y^3=0 ?

The solution for x^3(dy)/(dx)-x^2y-y^3=0 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=0

x^{3} \frac{d y}{d x} - x^{2} y - y^{3} = 0

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} = 0

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}}

\frac{d}{d x} (\frac{5}{1 - 9 x})

cos (x^{2} - 5)

\frac{d ^{2}}{d x ^{2}} (x^{3} y^{2} - 2 x^{2} y + 3 x)

\frac{x}{4}

\frac{d}{d x} (9 x^{3} - 4 y^{2} + 2 x y)

What is the solution for x^3(dy)/(dx)-x^2y-y^3=0 ?
The solution for x^3(dy)/(dx)-x^2y-y^3=0 is y= x/(sqrt(-2ln(x)+c_{1))},y=-x/(sqrt(-2ln(x)+c_{1))}