60.3.103 problem 1107

Internal problem ID [11113]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1107
Date solved : Tuesday, January 28, 2025 at 05:41:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.092 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 36

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

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