37.3.11 problem 10.4.10

Internal problem ID [6417]
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
Date solved : Tuesday, January 28, 2025 at 03:10:15 PM
CAS classification : [_Laguerre]

\begin{align*} x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+m y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (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)
 

\[ y = c_1 \operatorname {KummerM}\left (-m , 1, x\right )+c_2 \operatorname {KummerU}\left (-m , 1, x\right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 21

DSolve[x*D[y[x],{x,2}]+(1-x)*D[y[x],x]+m*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \operatorname {HypergeometricU}(-m,1,x)+c_2 \operatorname {LaguerreL}(m,x) \]