65.7.3 problem 14.1 (iii)

Internal problem ID [13767]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 14, Inhomogeneous second order linear equations. Exercises page 140
Problem number : 14.1 (iii)
Date solved : Tuesday, January 28, 2025 at 06:02:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&=3 \,{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

dsolve(diff(x(t),t$2)+diff(x(t),t)-2*x(t)=3*exp(-t),x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\left (2 c_{1} {\mathrm e}^{3 t}-3 \,{\mathrm e}^{t}+2 c_{2} \right ) {\mathrm e}^{-2 t}}{2} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 29

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

\[ x(t)\to -\frac {3 e^{-t}}{2}+c_1 e^{-2 t}+c_2 e^t \]