Internal problem ID [8690]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1110.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {y^{\prime \prime } x -y^{\prime } x -a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 23
dsolve(x*diff(diff(y(x),x),x)-x*diff(y(x),x)-a*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \KummerM \left (a +1, 2, x\right ) x +c_{2} \KummerU \left (a +1, 2, x\right ) x \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 36
DSolve[-(a*y[x]) - x*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 G_{1,2}^{2,0}\left (-x\left | {c} 1-a \\ 0,1 \\ \\ \right .\right )+c_1 x \, _1F_1(a+1;2;x) \\ \end{align*}