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

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

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

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

y = 3 6 (\frac{x}{2} + 1) + \frac{c _{1}}{x}

Solution steps

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

Solve Bernoulli ODE:

y = 3 6 (\frac{x}{2} + 1) + \frac{c _{1}}{x}

y = 3 6 (\frac{x}{2} + 1) + \frac{c _{1}}{x}

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

\int 7 x^{5} d x

x \to 0 + lim (tan^{2 x} (x))

e^{5 t} sin (2 t)

\int 25 + x^{2} d x

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