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

The solution for x^2(dy)/(dx)+2xy-y^3=0 is y=sqrt((5x)/(2+5c_{1)x^5)},y=-sqrt((5x)/(2+5c_{1)x^5)}

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x^2(dy)/(dx)+2xy-y^3=0

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

y = \frac{5 x}{2 + 5 c _{1} x ^{5}}, y = - \frac{5 x}{2 + 5 c _{1} x ^{5}}

Solution steps

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

Solve Bernoulli ODE:

y = \frac{5 x}{2 + 5 c _{1} x ^{5}}, y = - \frac{5 x}{2 + 5 c _{1} x ^{5}}

y = \frac{5 x}{2 + 5 c _{1} x ^{5}}, y = - \frac{5 x}{2 + 5 c _{1} x ^{5}}

\frac{d}{d x} (\frac{10}{x ^{7}})

\frac{d}{d t} (e^{- 5 t})

d u = - e^{- z} d z

x \to 0 - lim (\frac{1}{3 x})

\frac{\partial}{\partial x} (\frac{x}{x y} + \frac{y}{x y})

What is the solution for x^2(dy)/(dx)+2xy-y^3=0 ?
The solution for x^2(dy)/(dx)+2xy-y^3=0 is y=sqrt((5x)/(2+5c_{1)x^5)},y=-sqrt((5x)/(2+5c_{1)x^5)}