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

The solution for (dy)/(dx)=(x+2)/(y^2) is y=\sqrt[3]{(3x^2)/2+6x+c_{1}}

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

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

Solution steps

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

Solve separable ODE:

y^{^{'}} = \frac{4 x}{1 + 2 y}, y (9) = 0

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

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

x y^{2} cos (x) d x - 3 x^{2} y cos (x) d y = 0, y (1) = 1

\frac{d P}{d t} = 2 Pt, P (1) = 2

What is the solution for (dy)/(dx)=(x+2)/(y^2) ?
The solution for (dy)/(dx)=(x+2)/(y^2) is y=\sqrt[3]{(3x^2)/2+6x+c_{1}}