Internal problem ID [6584]
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]
Solve \begin {gather*} \boxed {c y^{\prime }-\frac {x a +b y^{2}}{r x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 98
dsolve(c*diff(y(x),x)=(a*x+b*y(x)^2)/(r*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\sqrt {\frac {x b a}{r^{2} c^{2}}}\, c r \left (\BesselY \left (1, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right ) c_{1} c r +\BesselJ \left (1, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right )\right )}{b \left (c_{1} c r \BesselY \left (0, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right )+\BesselJ \left (0, 2 \sqrt {\frac {x b a}{r^{2} c^{2}}}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.252 (sec). Leaf size: 160
DSolve[c*y'[x]==(a*x+b*y[x]^2)/(r*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\frac {2 \sqrt {a} c r \sqrt {x} Y_1\left (\frac {2 \sqrt {a} \sqrt {b} \sqrt {x}}{c r}\right )}{\sqrt {b}}+a c_1 x \, _0\tilde {F}_1\left (;2;-\frac {a b x}{c^2 r^2}\right )}{2 c r Y_0\left (\frac {2 \sqrt {a} \sqrt {b} \sqrt {x}}{c r}\right )+c c_1 r \, _0\tilde {F}_1\left (;1;-\frac {a b x}{c^2 r^2}\right )} \\ y(x)\to \frac {a x \, _0\tilde {F}_1\left (;2;-\frac {a b x}{c^2 r^2}\right )}{c r \, _0\tilde {F}_1\left (;1;-\frac {a b x}{c^2 r^2}\right )} \\ \end{align*}