Internal problem ID [8741]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}+x y^{\prime }-\left (x +a \right ) y=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = c_{1} \BesselI \left (2 \sqrt {a}, 2 \sqrt {x}\right )+c_{2} \BesselK \left (2 \sqrt {a}, 2 \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.024 (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 \text {Gamma}\left (1-2 \sqrt {a}\right ) I_{-2 \sqrt {a}}\left (2 \sqrt {x}\right )+(-1)^{\sqrt {a}} c_2 \text {Gamma}\left (2 \sqrt {a}+1\right ) I_{2 \sqrt {a}}\left (2 \sqrt {x}\right ) \\ \end{align*}