65.7.8 problem 14.1 (viii)

Internal problem ID [13772]
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)
Date solved : Tuesday, January 28, 2025 at 06:02:38 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{\prime \prime }+2 x^{\prime }+10 x&={\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 68

DSolve[D[x[t],{t,2}]+2*D[x[t],t]+10*x[t]==Exp[-t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-t} \left (\cos (3 t) \int _1^t-\frac {1}{3} \sin (3 K[2])dK[2]+\sin (3 t) \int _1^t\frac {1}{3} \cos (3 K[1])dK[1]+c_2 \cos (3 t)+c_1 \sin (3 t)\right ) \]