What is the solution for 3x^2ydx+(y+x^3)dy=0 ?

The solution for 3x^2ydx+(y+x^3)dy=0 is y=-x^3+sqrt(x^6+c_{1)},y=-x^3-sqrt(x^6+c_{1)}

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3x^2ydx+(y+x^3)dy=0

3 x^{2} y d x + (y + x^{3}) d y = 0

y = - x^{3} + x^{6} + c_{1}, y = - x^{3} - x^{6} + c_{1}

Solution steps

3 x^{2} y d x + (y + x^{3}) d y = 0

Solve exact ODE:

y = - x^{3} + x^{6} + c_{1}, y = - x^{3} - x^{6} + c_{1}

y = - x^{3} + x^{6} + c_{1}, y = - x^{3} - x^{6} + c_{1}

\frac{d}{d x} (ln (\frac{1}{1 + e ^{- x}}))

\frac{d}{d x} (\frac{x}{1 + x ^{\frac{3}{2}}})

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

\int_{0}^{x} t^{2} + t^{4} d t

\frac{d y}{d x} = y^{2} - 4

What is the solution for 3x^2ydx+(y+x^3)dy=0 ?
The solution for 3x^2ydx+(y+x^3)dy=0 is y=-x^3+sqrt(x^6+c_{1)},y=-x^3-sqrt(x^6+c_{1)}