Internal problem ID [8693]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1113.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {y^{\prime \prime } x +\left (b -x \right ) y^{\prime }-a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(x*diff(diff(y(x),x),x)+(b-x)*diff(y(x),x)-a*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \KummerM \left (a , b , x\right )+c_{2} \KummerU \left (a , b , x\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 24
DSolve[-(a*y[x]) + (b - x)*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \text {HypergeometricU}(a,b,x)+c_2 L_{-a}^{b-1}(x) \\ \end{align*}