Internal problem ID [8739]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1161.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -\left (a +x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-(x+a)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \operatorname {BesselI}\left (2 \sqrt {a}, 2 \sqrt {x}\right )+c_{2} \operatorname {BesselK}\left (2 \sqrt {a}, 2 \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 78
DSolve[(-a - x)*y[x] + x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (-1)^{-\sqrt {a}} c_1 \operatorname {Gamma}\left (1-2 \sqrt {a}\right ) \operatorname {BesselI}\left (-2 \sqrt {a},2 \sqrt {x}\right )+(-1)^{\sqrt {a}} c_2 \operatorname {Gamma}\left (2 \sqrt {a}+1\right ) \operatorname {BesselI}\left (2 \sqrt {a},2 \sqrt {x}\right ) \\ \end{align*}