Internal problem ID [11716]
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 (viii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }+2 x^{\prime }+10 x={\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(x(t),t$2)+2*diff(x(t),t)+10*x(t)=exp(-t),x(t), singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-t} \sin \left (3 t \right ) c_{2} +{\mathrm e}^{-t} \cos \left (3 t \right ) c_{1} +\frac {{\mathrm e}^{-t}}{9} \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 32
DSolve[x''[t]+2*x'[t]+10*x[t]==Exp[-t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{9} e^{-t} (9 c_2 \cos (3 t)+9 c_1 \sin (3 t)+1) \]