Internal problem ID [9427]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1097.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {y^{\prime \prime } x -y^{\prime }+a y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 70
dsolve(x*diff(diff(y(x),x),x)-diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {BesselJ}\left (1, 2 \sqrt {a}\, \sqrt {x}\right ) \sqrt {x}\, c_{1} +\operatorname {BesselY}\left (1, 2 \sqrt {a}\, \sqrt {x}\right ) \sqrt {x}\, c_{2} -\sqrt {a}\, x \left (c_{1} \operatorname {BesselJ}\left (0, 2 \sqrt {a}\, \sqrt {x}\right )+c_{2} \operatorname {BesselY}\left (0, 2 \sqrt {a}\, \sqrt {x}\right )\right )}{\sqrt {a}} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 45
DSolve[a*y[x] - y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 a x \left (c_1 \operatorname {BesselJ}\left (2,2 \sqrt {a} \sqrt {x}\right )-c_2 \operatorname {BesselY}\left (2,2 \sqrt {a} \sqrt {x}\right )\right ) \]