59.3.3 problem Kovacic 1985 paper. page 15. Weber equation

Internal problem ID [10005]
Book : Collection of Kovacic problems
Section : section 3. Problems from Kovacic related papers
Problem number : Kovacic 1985 paper. page 15. Weber equation
Date solved : Wednesday, March 05, 2025 at 08:02:06 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\left (\frac {x^{2}}{4}-\frac {11}{2}\right ) y \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 39

ode:=diff(diff(y(x),x),x) = (1/4*x^2-11/2)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-\frac {x^{2}}{4}} \left (15 \operatorname {hypergeom}\left (\left [-\frac {5}{2}\right ], \left [\frac {1}{2}\right ], \frac {x^{2}}{2}\right ) c_{2} +x c_{1} \left (x^{4}-10 x^{2}+15\right )\right )}{15} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 22

ode=D[y[x],{x,2}]== (1/4*x^2-1/2-5)*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 \operatorname {ParabolicCylinderD}(-6,i x)+c_1 \operatorname {ParabolicCylinderD}(5,x) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((11/2 - x**2/4)*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False