What is the solution for (dy)/(dx)=x(1+y)^2 ?

The solution for (dy)/(dx)=x(1+y)^2 is y=-2/(x^2+2c_{1)}-(x^2)/(x^2+2c_{1)}-(2c_{1})/(x^2+2c_{1)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(dy)/(dx)=x(1+y)^2

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

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

Solution steps

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

Solve separable ODE:

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

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

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