Internal problem ID [8677]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x -y^{\prime }+a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 31
dsolve(x*diff(diff(y(x),x),x)-diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \BesselJ \left (2, 2 \sqrt {a}\, \sqrt {x}\right )+c_{2} x \BesselY \left (2, 2 \sqrt {a}\, \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 38
DSolve[a*y[x] - y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a x \left (a c_1 x \, _0F_1(;3;-a x)-2 c_2 Y_2\left (2 \sqrt {a} \sqrt {x}\right )\right ) \\ \end{align*}