Internal problem ID [7680]
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]]
\[ \boxed {y^{\prime } x +y^{2} x +a=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(x*diff(y(x),x) + x*y(x)^2 + a=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sqrt {a}\, \left (\operatorname {BesselJ}\left (0, 2 \sqrt {a}\, \sqrt {x}\right ) c_{1} +\operatorname {BesselY}\left (0, 2 \sqrt {a}\, \sqrt {x}\right )\right )}{\sqrt {x}\, \left (c_{1} \operatorname {BesselJ}\left (1, 2 \sqrt {a}\, \sqrt {x}\right )+\operatorname {BesselY}\left (1, 2 \sqrt {a}\, \sqrt {x}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.217 (sec). Leaf size: 102
DSolve[x*y'[x] + x*y[x]^2 + a==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {a} \left (c_1 \, _0\tilde {F}_1(;1;-a x)+2 i Y_0\left (2 \sqrt {a} \sqrt {x}\right )\right )}{\sqrt {a} c_1 x \, _0\tilde {F}_1(;2;-a x)+2 i \sqrt {x} Y_1\left (2 \sqrt {a} \sqrt {x}\right )} \\ y(x)\to \frac {\, _0\tilde {F}_1(;1;-a x)}{x \, _0\tilde {F}_1(;2;-a x)} \\ \end{align*}