What is the solution for (dy}{dx}=(\frac{x^2)/y) ?

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

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(dy}{dx}=(\frac{x^2)/y)

\frac{d y}{d x} = (\frac{x ^{2}}{y})

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

Solution steps

\frac{d y}{d x} = (\frac{x ^{2}}{y})

Solve separable ODE:

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

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

- y^{3} + y^{^{'}} + 0.5 y = 0

y^{^{'}} = (x + 2) (y - 1), y (0) = 2

\frac{d y}{y} + y e^{c o s (x)} sin (x) d x = 0

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

\frac{d y}{d x} = 2 x^{4} y, y > 0

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