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

The solution for (dy)/(dx)= x/(y^2),y(0)=2 is y=\sqrt[3]{(3x^2)/2+8}

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(dy)/(dx)= x/(y^2),y(0)=2

\frac{d y}{d x} = \frac{x}{y ^{2}}, y (0) = 2

Solution steps

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

Solve separable ODE:

\frac{d y}{d t} - t y = y, y (1) = 3

y^{^{'}} = y^{- \frac{1}{3}}

\frac{d y}{d x} = \frac{5 e ^{x}}{e ^{y}}

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

\frac{d y}{d t} = \frac{t}{t ^{2} y + y}, y (0) = 8

What is the solution for (dy)/(dx)= x/(y^2),y(0)=2 ?
The solution for (dy)/(dx)= x/(y^2),y(0)=2 is y=\sqrt[3]{(3x^2)/2+8}