Internal problem ID [8297]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 717.
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 +a x +a -2 \sqrt {x^{2}+2 a x +a^{2}+4 y}}{2 x +2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.382 (sec). Leaf size: 33
dsolve(diff(y(x),x) = -1/2*(x^2+x+a*x+a-2*(x^2+2*a*x+a^2+4*y(x))^(1/2))/(x+1),y(x), singsol=all)
\[ c_{1}+\frac {a}{2}+2 \ln \left (x +1\right )-\sqrt {a^{2}+2 a x +x^{2}+4 y \relax (x )} = 0 \]
✓ Solution by Mathematica
Time used: 0.681 (sec). Leaf size: 35
DSolve[y'[x] == (-1/2*a - x/2 - (a*x)/2 - x^2/2 + Sqrt[a^2 + 2*a*x + x^2 + 4*y[x]])/(1 + x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{4} (a+x-2 \log (x+1)+2 c_1) (a+x+2 \log (x+1)-2 c_1) \\ \end{align*}