81.10.5 problem 14-5

Internal problem ID [21600]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 14. Second order homogeneous differential equations with constant coefficients. Page 297.
Problem number : 14-5
Date solved : Thursday, October 02, 2025 at 07:58:54 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

ode:=diff(diff(x(t),t),t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 t +c_2 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 12

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

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

✓ Sympy. Time used: 0.015 (sec). Leaf size: 7

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

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