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}}

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)}