54.3.257 problem 1273

Internal problem ID [12552]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1273
Date solved : Friday, October 03, 2025 at 03:38:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 17

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

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

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

ode=(1 - 4*m^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,m}(x)+c_2 W_{k,m}(x) \end{align*}

✗ Sympy

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

False