Internal problem ID [8254]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 674.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]]]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 x +2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.333 (sec). Leaf size: 27
dsolve(diff(y(x),x) = -1/2*(x^2-x-2-2*(x^2-4*x+4*y(x))^(1/2))/(x+1),y(x), singsol=all)
\[ c_{1}+2 \ln \left (x +1\right )-1-\sqrt {x^{2}+4 y \relax (x )-4 x} = 0 \]
✓ Solution by Mathematica
Time used: 0.499 (sec). Leaf size: 32
DSolve[y'[x] == (1 + x/2 - x^2/2 + Sqrt[-4*x + x^2 + 4*y[x]])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{4}+x+\log ^2(x+1)-2 c_1 \log (x+1)+c_1{}^2 \\ \end{align*}