57.3.4 problem 4(a)

Internal problem ID [14320]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.2 Antiderivatives. Exercises page 19
Problem number : 4(a)
Date solved : Thursday, October 02, 2025 at 09:31:29 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ x = \frac {\left (-2 t -1\right ) {\mathrm e}^{-2 t}}{4}+c_1 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 22

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

\begin{align*} x(t)&\to -\frac {1}{4} e^{-2 t} (2 t+1)+c_1 \end{align*}

✓ Sympy. Time used: 0.092 (sec). Leaf size: 20

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

\[ x{\left (t \right )} = C_{1} - \frac {t e^{- 2 t}}{2} - \frac {e^{- 2 t}}{4} \]