80.5.39 problem C 15

Internal problem ID [21260]
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 : C 15
Date solved : Thursday, October 02, 2025 at 07:27:25 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ x = {\mathrm e}^{t} c_1 -\frac {t^{2}}{2}-t +c_2 \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 24

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

\begin{align*} x(t)&\to -\frac {t^2}{2}-t+c_1 e^t+c_2 \end{align*}

✓ Sympy. Time used: 0.081 (sec). Leaf size: 15

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

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