Internal problem ID [9433]
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]]
\[ \boxed {y^{\prime \prime } x -2 y^{\prime }+a y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 80
dsolve(x*diff(diff(y(x),x),x)-2*diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\sqrt {x}\, \left (c_{1} \left (a x -2\right ) \operatorname {BesselJ}\left (1, 2 \sqrt {a}\, \sqrt {x}\right )+c_{2} \left (a x -2\right ) \operatorname {BesselY}\left (1, 2 \sqrt {a}\, \sqrt {x}\right )+2 \sqrt {a}\, \sqrt {x}\, \left (c_{1} \operatorname {BesselJ}\left (0, 2 \sqrt {a}\, \sqrt {x}\right )+c_{2} \operatorname {BesselY}\left (0, 2 \sqrt {a}\, \sqrt {x}\right )\right )\right )}{a} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 56
DSolve[a*y[x] - 2*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 a^{3/2} x^{3/2} \left (3 c_1 \operatorname {BesselJ}\left (3,2 \sqrt {a} \sqrt {x}\right )-i c_2 \operatorname {BesselY}\left (3,2 \sqrt {a} \sqrt {x}\right )\right ) \]