63.3.4 problem 4(a)

Internal problem ID [12960]
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 : Wednesday, March 05, 2025 at 08:54:57 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 24

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

\[ x(t)\to \int _1^te^{-2 K[1]} K[1]dK[1]+c_1 \]

✓ Sympy. Time used: 0.167 (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)
 

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