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

The solution for (dy)/(dx)=(x^2-2)/(3y) is y=(sqrt(2x^3-12x+c_{1)})/3 ,y=-(sqrt(2x^3-12x+c_{1)})/3

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(dy)/(dx)=(x^2-2)/(3y)

\frac{d y}{d x} = \frac{x ^{2} - 2}{3 y}

y = \frac{2 x ^{3} - 12 x + c _{1}}{3}, y = - \frac{2 x ^{3} - 12 x + c _{1}}{3}

Solution steps

\frac{d y}{d x} = \frac{x ^{2} - 2}{3 y}

Solve separable ODE:

y = \frac{2 x ^{3} - 12 x + c _{1}}{3}, y = - \frac{2 x ^{3} - 12 x + c _{1}}{3}

y = \frac{2 x ^{3} - 12 x + c _{1}}{3}, y = - \frac{2 x ^{3} - 12 x + c _{1}}{3}

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What is the solution for (dy)/(dx)=(x^2-2)/(3y) ?
The solution for (dy)/(dx)=(x^2-2)/(3y) is y=(sqrt(2x^3-12x+c_{1)})/3 ,y=-(sqrt(2x^3-12x+c_{1)})/3