80.1.18 problem 16 (a)

Internal problem ID [21136]
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 1. First order linear differential equations. Excercise 1.5 at page 13
Problem number : 16 (a)
Date solved : Thursday, October 02, 2025 at 07:09:45 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} x \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 13

ode:=diff(x(t),t)-x(t) = 1/2*t; 
ic:=[x(0) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = -\frac {t}{2}-\frac {1}{2}+\frac {3 \,{\mathrm e}^{t}}{2} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 19

ode=D[x[t],t]-x[t]==1/2*t; 
ic={x[0]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{2} \left (-t+3 e^t-1\right ) \end{align*}

✓ Sympy. Time used: 0.074 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-t/2 - x(t) + Derivative(x(t), t),0) 
ics = {x(0): 1} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = - \frac {t}{2} + \frac {3 e^{t}}{2} - \frac {1}{2} \]