What is the solution for (dy)/(dx)+y=xy^3 ?

The solution for (dy)/(dx)+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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(dy)/(dx)+y=xy^3

\frac{d y}{d x} + 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

\frac{d y}{d 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}}

x \to 22 lim (2 x^{2} - 3 x - 5)

n = 1 \sum \infty \frac{3}{3 ^{n}}

n = 0 \sum \infty \frac{1}{n}

\int \frac{t ^{2}}{t ^{3} + 7} d t

\frac{d y}{d x} + 8 y - 8 e^{- 5 x} = 0, y (0) = \frac{5}{3}

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