54.3.94 problem 1108

Internal problem ID [12389]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1108
Date solved : Friday, October 03, 2025 at 03:18:50 AM
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*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 26

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

\[ y = {\mathrm e}^{-x} \left (\operatorname {KummerU}\left (b , a +b , x\right ) c_2 +\operatorname {KummerM}\left (b , a +b , x\right ) c_1 \right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to e^{-x} (c_1 \operatorname {HypergeometricU}(b,a+b,x)+c_2 L_{-b}^{a+b-1}(x)) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(a*y(x) + x*Derivative(y(x), (x, 2)) + (a + b + x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None