68.2.1 problem Problem 3.7(a)

Internal problem ID [14075]
Book : Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto. Cambridge Univ. Press 2003
Section : Chapter 3 Bessel functions. Problems page 89
Problem number : Problem 3.7(a)
Date solved : Monday, March 31, 2025 at 12:02:44 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }-x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)-x^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\operatorname {BesselK}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_2 +\operatorname {BesselI}\left (\frac {1}{4}, \frac {x^{2}}{2}\right ) c_1 \right ) \sqrt {x} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 37

ode=D[y[x],{x,2}]-x^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 \operatorname {ParabolicCylinderD}\left (-\frac {1}{2},i \sqrt {2} x\right )+c_1 \operatorname {ParabolicCylinderD}\left (-\frac {1}{2},\sqrt {2} x\right ) \]

✗ Sympy

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

False