7.17.12 problem 12

Internal problem ID [525]
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 : 12
Date solved : Saturday, March 29, 2025 at 04:55:49 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x y^{\prime \prime }+4 x^{3} y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 23

ode:=x*diff(diff(y(x),x),x)+4*x^3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 59

ode=D[y[x],{x,2}]+4*x^3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt [5]{\frac {2}{5}} \sqrt {x} \left (c_1 \operatorname {Gamma}\left (\frac {4}{5}\right ) \operatorname {BesselJ}\left (-\frac {1}{5},\frac {4 x^{5/2}}{5}\right )+c_2 \operatorname {Gamma}\left (\frac {6}{5}\right ) \operatorname {BesselJ}\left (\frac {1}{5},\frac {4 x^{5/2}}{5}\right )\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**3*y(x) + x*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False