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

The solution for x^3+2y(dy)/(dx)=0 is y=(sqrt(c_{1)-x^4})/2 ,y=-(sqrt(c_{1)-x^4})/2

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

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

y = \frac{c _{1} - x ^{4}}{2}, y = - \frac{c _{1} - x ^{4}}{2}

Solution steps

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

Solve separable ODE:

y = \frac{c _{1} - x ^{4}}{2}, y = - \frac{c _{1} - x ^{4}}{2}

y = \frac{c _{1} - x ^{4}}{2}, y = - \frac{c _{1} - x ^{4}}{2}

\frac{df}{d x} + f (x)^{2} = 0

\frac{d y}{d x} = \frac{y ln ( y )}{cot ( x )}

y (4 + x^{2}) d y - x (2 + y^{2}) d x = 0

\frac{d y}{d x} x ln (x) - y = 0, y (2) = ln (4)

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

What is the solution for x^3+2y(dy)/(dx)=0 ?
The solution for x^3+2y(dy)/(dx)=0 is y=(sqrt(c_{1)-x^4})/2 ,y=-(sqrt(c_{1)-x^4})/2