Internal problem ID [4566]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.4, ODEs with variable Coefficients. Second
order and Homogeneous. page 318
Problem number: 10.4.10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+m y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 21
dsolve(x*diff(y(x),x$2)+(1-x)*diff(y(x),x)+m*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \KummerM \left (-m , 1, x\right )+c_{2} \KummerU \left (-m , 1, x\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 21
DSolve[x*y''[x]+(1-x)*y'[x]+m*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \text {HypergeometricU}(-m,1,x)+c_2 \text {LaguerreL}(m,x) \\ \end{align*}