63.4.28 problem 23

Internal problem ID [13071]
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 1.3.1 Separable equations. Exercises page 26
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 04:51:20 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 16

dsolve([diff(x(t)*exp(2*t),t)=exp(-t),x(0) = 3],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 18

DSolve[{D[x[t]*Exp[2*t],t]==Exp[-t],{x[0]==3}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-3 t} \left (4 e^t-1\right ) \]