23.3.445 problem 450

Internal problem ID [6159]
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 : 450
Date solved : Friday, October 03, 2025 at 01:48:03 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (4 k x -4 p^{2}-x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 17

ode:=(4*k*x-4*p^2-x^2+1)*y(x)+4*x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \operatorname {WhittakerM}\left (k , p , x\right )+c_2 \operatorname {WhittakerW}\left (k , p , x\right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 20

ode=(1 - 4*p^2 + 4*k*x - x^2)*y[x] + 4*x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 M_{k,p}(x)+c_2 W_{k,p}(x) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
k = symbols("k") 
p = symbols("p") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) + (4*k*x - 4*p**2 - x**2 + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False