63.3.4 problem 4(a)

Internal problem ID [13039]
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 : Tuesday, January 28, 2025 at 04:49:57 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[x[t],t]==t*Exp[-2*t],x[t],t,IncludeSingularSolutions -> True]
 

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