60.3.109 problem 1113

Internal problem ID [11119]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1113
Date solved : Tuesday, January 28, 2025 at 05:41:14 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: 0.098 (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)
 

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 24

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

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