Internal problem ID [10684]
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 (iv).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }+x^{\prime }-2 x-{\mathrm e}^{t}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(x(t),t$2)+diff(x(t),t)-2*x(t)=exp(t),x(t), singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-2 t}+\frac {t \,{\mathrm e}^{t}}{3} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 29
DSolve[x''[t]+x'[t]-2*x[t]==Exp[t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{-2 t}+e^t \left (\frac {t}{3}-\frac {1}{9}+c_2\right ) \\ \end{align*}