80.5.53 problem D 2 (b)

Internal problem ID [21274]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 5. Second order equations. Excercise 5.9 at page 119
Problem number : D 2 (b)
Date solved : Thursday, October 02, 2025 at 07:27:34 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{\prime \prime }+2 t^{3} x&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=diff(diff(x(t),t),t)+2*t^3*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \sqrt {t}\, \left (\operatorname {BesselY}\left (\frac {1}{5}, \frac {2 \sqrt {2}\, t^{{5}/{2}}}{5}\right ) c_2 +\operatorname {BesselJ}\left (\frac {1}{5}, \frac {2 \sqrt {2}\, t^{{5}/{2}}}{5}\right ) c_1 \right ) \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 72

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

\begin{align*} x(t)&\to \frac {\sqrt [10]{2} \sqrt {t} \left (c_1 \operatorname {Gamma}\left (\frac {4}{5}\right ) \operatorname {BesselJ}\left (-\frac {1}{5},\frac {2}{5} \sqrt {2} t^{5/2}\right )+c_2 \operatorname {Gamma}\left (\frac {6}{5}\right ) \operatorname {BesselJ}\left (\frac {1}{5},\frac {2}{5} \sqrt {2} t^{5/2}\right )\right )}{\sqrt [5]{5}} \end{align*}

✗ Sympy

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

False