Internal problem ID [7337]
Book: First order enumerated odes
Section: section 1
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {y^{\prime } c -\frac {x a +b y^{2}}{r x}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 94
dsolve(c*diff(y(x),x)=(a*x+b*y(x)^2)/(r*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sqrt {\frac {x b a}{r^{2} c^{2}}}\, c r \left (\operatorname {BesselY}\left (1, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right ) c_{1} +\operatorname {BesselJ}\left (1, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right )\right )}{b \left (c_{1} \operatorname {BesselY}\left (0, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right )+\operatorname {BesselJ}\left (0, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.295 (sec). Leaf size: 207
DSolve[c*y'[x]==(a*x+b*y[x]^2)/(r*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {a} \sqrt {x} \left (2 \operatorname {BesselY}\left (1,\frac {2 \sqrt {a} \sqrt {b} \sqrt {x}}{c r}\right )+c_1 \operatorname {BesselJ}\left (1,\frac {2 \sqrt {a} \sqrt {b} \sqrt {x}}{c r}\right )\right )}{\sqrt {b} \left (2 \operatorname {BesselY}\left (0,\frac {2 \sqrt {a} \sqrt {b} \sqrt {x}}{c r}\right )+c_1 \operatorname {BesselJ}\left (0,\frac {2 \sqrt {a} \sqrt {b} \sqrt {x}}{c r}\right )\right )} \\ y(x)\to \frac {\sqrt {a} \sqrt {x} \operatorname {BesselJ}\left (1,\frac {2 \sqrt {a} \sqrt {b} \sqrt {x}}{c r}\right )}{\sqrt {b} \operatorname {BesselJ}\left (0,\frac {2 \sqrt {a} \sqrt {b} \sqrt {x}}{c r}\right )} \\ \end{align*}