Internal problem ID [8674]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1094.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+y^{\prime }+a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(x*diff(diff(y(x),x),x)+diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \BesselJ \left (0, 2 \sqrt {a}\, \sqrt {x}\right )+c_{2} \BesselY \left (0, 2 \sqrt {a}\, \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 33
DSolve[a*y[x] + y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \, _0\tilde {F}_1(;1;-a x)+2 c_2 Y_0\left (2 \sqrt {a} \sqrt {x}\right ) \\ \end{align*}