65.7.12 problem 14.2

Internal problem ID [13776]
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 : 14.2
Date solved : Tuesday, January 28, 2025 at 06:03:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+x^{\prime }-2 x&=12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(diff(x(t),t$2)+diff(x(t),t)-2*x(t)=12*exp(-t)-6*exp(t),x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.180 (sec). Leaf size: 34

DSolve[D[x[t],{t,2}]+D[x[t],t]-2*x[t]==12*Exp[-t]-6*Exp[t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-2 t} \left (-6 e^t+e^{3 t} \left (-2 t+\frac {2}{3}+c_2\right )+c_1\right ) \]