Internal problem ID [11713]
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 (v).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }+2 x^{\prime }+x={\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(x(t),t$2)+2*diff(x(t),t)+x(t)=exp(-t),x(t), singsol=all)
\[ x \left (t \right ) = c_{1} t \,{\mathrm e}^{-t}+\frac {{\mathrm e}^{-t} t^{2}}{2}+c_{2} {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 27
DSolve[x''[t]+2*x'[t]+x[t]==Exp[-t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{2} e^{-t} \left (t^2+2 c_2 t+2 c_1\right ) \]