23.3.209 problem 211

Internal problem ID [5923]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 211
Date solved : Friday, October 03, 2025 at 01:45:23 AM
CAS classification : [_Laguerre]

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

✓ Maple. Time used: 0.026 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 24

ode=-(a*y[x]) + (c - 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,c,x)+c_2 L_{-a}^{c-1}(x) \end{align*}

✗ Sympy

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

ValueError : Expected Expr or iterable but got None