80.5.52 problem D 2 (a)

Internal problem ID [21273]
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 (a)
Date solved : Thursday, October 02, 2025 at 07:27:34 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x&=0 \end{align*}

✗ Maple

ode:=diff(diff(x(t),t),t)+(t^6+3*t^5+1)^(1/2)*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],{t,2}]+Sqrt[t^6+3*t^5+1]*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(sqrt(t**6 + 3*t**5 + 1)*x(t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

False