Internal problem ID [8683]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1103.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x -2 y^{\prime }+a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 35
dsolve(x*diff(diff(y(x),x),x)-2*diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{\frac {3}{2}} \BesselJ \left (3, 2 \sqrt {a}\, \sqrt {x}\right )+c_{2} x^{\frac {3}{2}} \BesselY \left (3, 2 \sqrt {a}\, \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 51
DSolve[a*y[x] - 2*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a^3 c_1 x^3 \, _0F_1(;4;-a x)-2 i a^{3/2} c_2 x^{3/2} Y_3\left (2 \sqrt {a} \sqrt {x}\right ) \\ \end{align*}