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

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

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y^'=(x^2)/(y(2+x^3))

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{\partial}{\partial x} (3 e^{x} cos (y))

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\int_{4}^{4} e^{- x^{2}} d x

\frac{d}{d y} (3 x + 4 y)

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