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

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

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y^'+y=xy^3

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

y = \frac{2}{2 x + 1 + 2 c _{1} e ^{2 x}}, y = - \frac{2}{2 x + 1 + 2 c _{1} e ^{2 x}}

Solution steps

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

Solve Bernoulli ODE:

y = \frac{2}{2 x + 1 + 2 c _{1} e ^{2 x}}, y = - \frac{2}{2 x + 1 + 2 c _{1} e ^{2 x}}

y = \frac{2}{2 x + 1 + 2 c _{1} e ^{2 x}}, y = - \frac{2}{2 x + 1 + 2 c _{1} e ^{2 x}}

y = (\frac{x ^{2} + 3}{x ^{2} - 3})^{4}

x \to 1 lim (- x)

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

\frac{e ^{7 x}}{ln ( 6 x )}

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

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