What is the solution for y^3-(2x+6)+3xy^2y^'=0 ?

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

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y^3-(2x+6)+3xy^2y^'=0

y^{3} - (2 x + 6) + 3 x y^{2} y^{^{'}} = 0

Solution steps

y^{3} - (2 x + 6) + 3 x y^{2} y^{'} (x) = 0

Solve Bernoulli ODE:

g (x) = 13 x

x \to - 1 + lim (2 - x)

x \to 6 + lim (\frac{2}{x - 6})

\int \frac{x ^{2}}{( x ^{2} - 4 ) ^{\frac{3}{2}}} d x

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

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