85.1.16 problem 11 (b)

Internal problem ID [22421]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 11 (b)
Date solved : Thursday, October 02, 2025 at 08:39:09 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=4 \,{\mathrm e}^{-t}-2 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 15

ode:=diff(x(t),t) = 4*exp(-t)-2; 
ic:=[x(0) = 3]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = -4 \,{\mathrm e}^{-t}-2 t +7 \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 17

ode=D[x[t],{t,1}]==4*Exp[-t]-2; 
ic={x[0]==3}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -2 t-4 e^{-t}+7 \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(Derivative(x(t), t) + 2 - 4*exp(-t),0) 
ics = {x(0): 3} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = - 2 t + 7 - 4 e^{- t} \]