60.3.104 problem 1108

Internal problem ID [11114]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1108
Date solved : Tuesday, January 28, 2025 at 05:41:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.115 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 33

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

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