What is the solution for (dy)/(dx)=(((1+y)^2))/((1+x)^3) ?

The solution for (dy)/(dx)=(((1+y)^2))/((1+x)^3) is

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(dy)/(dx)=(((1+y)^2))/((1+x)^3)

\frac{d y}{d x} = \frac{( ( 1 + y ) ^{2} )}{( 1 + x ) ^{3}}

y = - \frac{2 x ^{2}}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{2 c _{1} x ^{2}}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{4 x}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{4 c _{1} x}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{2 c _{1}}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{1}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}}

Solution steps

\frac{d y}{d x} = \frac{( ( 1 + y ) ^{2} )}{( 1 + x ) ^{3}}

Solve separable ODE:

y = - \frac{2 x ^{2}}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{2 c _{1} x ^{2}}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{4 x}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{4 c _{1} x}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{2 c _{1}}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{1}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}}

y = - \frac{2 x ^{2}}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{2 c _{1} x ^{2}}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{4 x}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{4 c _{1} x}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{2 c _{1}}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}} - \frac{1}{- 1 + 2 c _{1} x ^{2} + 4 c _{1} x + 2 c _{1}}

What is the solution for (dy)/(dx)=(((1+y)^2))/((1+x)^3) ?
The solution for (dy)/(dx)=(((1+y)^2))/((1+x)^3) is