65.1.10 problem 5.4 (v)

Internal problem ID [13713]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 5, Trivial differential equations. Exercises page 33
Problem number : 5.4 (v)
Date solved : Tuesday, January 28, 2025 at 05:55:49 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 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(3*t),t)=exp(-t),x(0) = 3],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 18

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

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