23.3.110 problem 112

Internal problem ID [5824]
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 : 112
Date solved : Friday, October 03, 2025 at 01:43:57 AM
CAS classification : [_Hermite]

\begin{align*} n y-x y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 35

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

\[ y = x \left (\operatorname {KummerM}\left (\frac {1}{2}-\frac {n}{2}, \frac {3}{2}, \frac {x^{2}}{2}\right ) c_1 +\operatorname {KummerU}\left (\frac {1}{2}-\frac {n}{2}, \frac {3}{2}, \frac {x^{2}}{2}\right ) c_2 \right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 37

ode=n*y[x] - x*D[y[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 {HermiteH}\left (n,\frac {x}{\sqrt {2}}\right )+c_2 \operatorname {Hypergeometric1F1}\left (-\frac {n}{2},\frac {1}{2},\frac {x^2}{2}\right ) \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) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False