54.3.99 problem 1113

Internal problem ID [12394]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1113
Date solved : Friday, October 03, 2025 at 03:18:51 AM
CAS classification : [_Laguerre]

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 24

ode=-(a*y[x]) + (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 c_1 \operatorname {HypergeometricU}(a,b,x)+c_2 L_{-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)) + (b - x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None