23.3.202 problem 204

Internal problem ID [5916]
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 : 204
Date solved : Friday, October 03, 2025 at 01:45:20 AM
CAS classification : [_Laguerre]

\begin{align*} n y+\left (1-x \right ) y^{\prime }+x y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 21

ode:=n*y(x)+(1-x)*diff(y(x),x)+x*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \operatorname {KummerM}\left (-n , 1, x\right )+c_2 \operatorname {KummerU}\left (-n , 1, x\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 21

ode=n*y[x] + (1 - 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}(-n,1,x)+c_2 \operatorname {LaguerreL}(n,x) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
n = symbols("n") 
y = Function("y") 
ode = Eq(n*y(x) + x*Derivative(y(x), (x, 2)) + (1 - x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False