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)}

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(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}}

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

\frac{d y}{d x} = \frac{sin ( x )}{sin ( y )}

H (x) (x)^{2} x^{2} d x - 2 x^{3} d H (x) = 0

y^{^{'}} = x (10 - y)

\frac{d y}{d x} = - \frac{5}{7} x^{3} y^{2}

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)}