Internal problem ID [8985]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 650.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
\[ \boxed {y^{\prime }-x \sqrt {x^{2}+2 a x +a^{2}+4 y}=-\frac {x}{2}-\frac {a}{2}} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 35
dsolve(diff(y(x),x) = -1/2*x-1/2*a+x*(x^2+2*a*x+a^2+4*y(x))^(1/2),y(x), singsol=all)
\[ c_{1} +\frac {a^{2}}{4}+\frac {x^{2}}{4}+\frac {1}{16}-\frac {\sqrt {x^{2}+2 a x +a^{2}+4 y \left (x \right )}}{4} = 0 \]
✓ Solution by Mathematica
Time used: 0.658 (sec). Leaf size: 39
DSolve[y'[x] == -1/2*a - x/2 + x*Sqrt[a^2 + 2*a*x + x^2 + 4*y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (-a^2-2 a x+x^4-(1+4 c_1) x^2+4 c_1{}^2\right ) \]