Internal problem ID [12031]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }+x^{\prime }-2 x=3 \,{\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(x(t),t$2)+diff(x(t),t)-2*x(t)=3*exp(-t),x(t), singsol=all)
\[ x \left (t \right ) = -\frac {\left (-2 c_{2} {\mathrm e}^{3 t}+3 \,{\mathrm e}^{t}-2 c_{1} \right ) {\mathrm e}^{-2 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 29
DSolve[x''[t]+x'[t]-2*x[t]==3*Exp[-t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -\frac {3 e^{-t}}{2}+c_1 e^{-2 t}+c_2 e^t \]