60.3.106 problem 1110

Internal problem ID [11116]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1110
Date solved : Tuesday, January 28, 2025 at 05:41:13 PM
CAS classification : [_Laguerre]

\begin{align*} x y^{\prime \prime }-x y^{\prime }-a y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 23

dsolve(x*diff(diff(y(x),x),x)-x*diff(y(x),x)-a*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.169 (sec). Leaf size: 36

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

\[ y(x)\to c_2 G_{1,2}^{2,0}\left (-x\left | \begin {array}{c} 1-a \\ 0,1 \\ \end {array} \right .\right )+c_1 x \operatorname {Hypergeometric1F1}(a+1,2,x) \]