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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

x \to - 1 lim (x^{3} - 3 x^{2} - 2 x + 1)

\int_{0}^{2} x + 2 - x^{2} d x

\frac{d}{d t} (\frac{t ^{3}}{4 - 3 t + 5})

x^{2} (1 - 2 x)

\frac{d}{d x} (\frac{1}{csc ( x )})

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