7.8 problem 14.1 (viii)

Internal problem ID [12036]

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: 26

dsolve(diff(x(t),t$2)+2*diff(x(t),t)+10*x(t)=exp(-t),x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {{\mathrm e}^{-t} \left (9 c_{2} \sin \left (3 t \right )+9 c_{1} \cos \left (3 t \right )+1\right )}{9} \]

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]
 

\[ x(t)\to \frac {1}{9} e^{-t} (9 c_2 \cos (3 t)+9 c_1 \sin (3 t)+1) \]