Internal problem ID [7681]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 100.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Riccati, _special]]
Solve \begin {gather*} \boxed {x y^{\prime }+x y^{2}+a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 59
dsolve(x*diff(y(x),x) + x*y(x)^2 + a=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {a}\, \left (\BesselJ \left (0, 2 \sqrt {a}\, \sqrt {x}\right ) c_{1}+\BesselY \left (0, 2 \sqrt {a}\, \sqrt {x}\right )\right )}{\sqrt {x}\, \left (c_{1} \BesselJ \left (1, 2 \sqrt {a}\, \sqrt {x}\right )+\BesselY \left (1, 2 \sqrt {a}\, \sqrt {x}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.198 (sec). Leaf size: 45
DSolve[x*y'[x] + x*y[x]^2 + a==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\, _0\tilde {F}_1(;1;-a x)}{x \, _0\tilde {F}_1(;2;-a x)} \\ y(x)\to \frac {\, _0\tilde {F}_1(;1;-a x)}{x \, _0\tilde {F}_1(;2;-a x)} \\ \end{align*}