61.28.10 problem 70

Internal problem ID [12570]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-3
Problem number : 70
Date solved : Tuesday, January 28, 2025 at 08:02:23 PM
CAS classification : [_Laguerre]

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

✓ Solution by Maple

Time used: 0.146 (sec). Leaf size: 17

dsolve(x*diff(y(x),x$2)+(b-x)*diff(y(x),x)-a*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \operatorname {KummerM}\left (a , b , x\right )+c_{2} \operatorname {KummerU}\left (a , b , x\right ) \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 24

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

\[ y(x)\to c_1 \operatorname {HypergeometricU}(a,b,x)+c_2 L_{-a}^{b-1}(x) \]