What is the solution for y^2(dy)/(dx)+2xy^3=6x,y(0)=1 ?

The solution for y^2(dy)/(dx)+2xy^3=6x,y(0)=1 is y=\sqrt[3]{-2e^{-3x^2}+3}

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y^2(dy)/(dx)+2xy^3=6x,y(0)=1

y^{2} \frac{d y}{d x} + 2 x y^{3} = 6 x, y (0) = 1

Solution steps

y^{2} \frac{d y}{d x} + 2 x y^{3} = 6 x

Solve separable ODE:

\frac{d y}{d x} = 3.2 y^{\frac{2}{3}}, x (0) = 1, y (0) = 13

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

3 y^{^{'}} - 4 y - 91 = 2 y^{^{'}}

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

1 x \frac{d y}{d x} + y = \frac{5}{y ^{2}}

What is the solution for y^2(dy)/(dx)+2xy^3=6x,y(0)=1 ?
The solution for y^2(dy)/(dx)+2xy^3=6x,y(0)=1 is y=\sqrt[3]{-2e^{-3x^2}+3}