80.5.64 problem D 15

Internal problem ID [21285]
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 15
Date solved : Thursday, October 02, 2025 at 07:27:47 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ x = \frac {c_1 \,t^{3}+c_2}{t} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

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

\begin{align*} x(t)&\to \frac {c_2 t^3+c_1}{t} \end{align*}

✓ Sympy. Time used: 0.025 (sec). Leaf size: 10

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

\[ x{\left (t \right )} = \frac {C_{1}}{t} + C_{2} t^{2} \]