What is the solution for xy^'+y=xy^3 ?

The solution for xy^'+y=xy^3 is y= 1/(sqrt(x(2+c_{1)x))},y=-1/(sqrt(x(2+c_{1)x))}

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xy^'+y=xy^3

x y^{^{'}} + y = x y^{3}

y = \frac{1}{x ( 2 + c _{1} x )}, y = - \frac{1}{x ( 2 + c _{1} x )}

Solution steps

x y^{'} (x) + y = x y^{3}

Solve Bernoulli ODE:

y = \frac{1}{x ( 2 + c _{1} x )}, y = - \frac{1}{x ( 2 + c _{1} x )}

y = \frac{1}{x ( 2 + c _{1} x )}, y = - \frac{1}{x ( 2 + c _{1} x )}

n = 0 \sum \infty (\frac{3}{8})^{\frac{n}{2}}

\frac{d v}{d x} = x

y^{^{'''}} + y^{^{''}} = 0

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

1 0^{- 3} y^{^{'}} + 10 y = 220 cos (50 t)

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