What is the solution for y^'+(1+y^3)/(xy^2(1+x^2))=0 ?

The solution for y^'+(1+y^3)/(xy^2(1+x^2))=0 is y=(\sqrt[3]{c_{1}(x^2+1)^{3/2}-x^3})/x

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y^'+(1+y^3)/(xy^2(1+x^2))=0

y^{^{'}} + \frac{1 + y ^{3}}{x y ^{2} ( 1 + x ^{2} )} = 0

y = \frac{3 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} - x ^{3}}{x}

Solution steps

y^{'} (x) + \frac{1 + y ^{3}}{x y ^{2} ( 1 + x ^{2} )} = 0

Solve separable ODE:

y = \frac{3 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} - x ^{3}}{x}

y = \frac{3 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} - x ^{3}}{x}

\frac{d y}{d x} = - \frac{5}{3} x^{3} y^{6}

\frac{d x}{d y} = y - 4 x y

\frac{d y}{d t} + 2 (t + 1) y^{2} = 0, y (0) = - \frac{1}{15}

10 y^{^{'}} - 2 y - 63 = 9 y^{^{'}}

y^{5} \frac{d y}{d x} = 4 x^{4} y^{6} - 12 x^{4}

What is the solution for y^'+(1+y^3)/(xy^2(1+x^2))=0 ?
The solution for y^'+(1+y^3)/(xy^2(1+x^2))=0 is y=(\sqrt[3]{c_{1}(x^2+1)^{3/2}-x^3})/x