1.17.11 problem 11

Internal problem ID [524]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.6 (Applications of Bessel functions). Problems at page 261
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 03:59:52 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }+x^{4} y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)+x^4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\operatorname {BesselY}\left (\frac {1}{6}, \frac {x^{3}}{3}\right ) c_2 +\operatorname {BesselJ}\left (\frac {1}{6}, \frac {x^{3}}{3}\right ) c_1 \right ) \sqrt {x} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 53

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

\begin{align*} y(x)&\to \frac {\sqrt {x} \left (c_1 \operatorname {Gamma}\left (\frac {5}{6}\right ) \operatorname {BesselJ}\left (-\frac {1}{6},\frac {x^3}{3}\right )+c_2 \operatorname {Gamma}\left (\frac {7}{6}\right ) \operatorname {BesselJ}\left (\frac {1}{6},\frac {x^3}{3}\right )\right )}{\sqrt [6]{6}} \end{align*}

✗ Sympy

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

False