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

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

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

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

Solution steps

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

Solve separable ODE:

y d x + (1 + x^{2}) arctan (x) d y = 0

y^{^{'}} cos (x) + (3 y - 1) sec (x) = 0, y (\frac{1}{4} π) = \frac{4}{3}

x^{^{'}} = \frac{1 + x}{1 + t}

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

y^{^{'}} = t^{2} y, y (0) = 1

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