Internal problem ID [8316]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 736.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x^{2}+2 x +x^{4}-2 x^{2} y-1+y^{2}}{x +1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 47
dsolve(diff(y(x),x) = (2*x^2+2*x+x^4-2*x^2*y(x)-1+y(x)^2)/(x+1),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{4}+2 c_{1} x^{3}-c_{1} x^{2}-2 c_{1} x +x^{2}-2 c_{1}+1}{c_{1} x^{2}+2 c_{1} x +1} \]
✓ Solution by Mathematica
Time used: 0.326 (sec). Leaf size: 38
DSolve[y'[x] == (-1 + 2*x + 2*x^2 + x^4 - 2*x^2*y[x] + y[x]^2)/(1 + x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2-\frac {2 (x+1)^2}{x (x+2)-2 c_1}+1 \\ y(x)\to x^2+1 \\ \end{align*}