65.7.10 problem 14.1 (x)

Internal problem ID [13774]
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 (x)
Date solved : Tuesday, January 28, 2025 at 06:03:01 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+6 x^{\prime }+10 x&={\mathrm e}^{-2 t} \cos \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 32

dsolve(diff(x(t),t$2)+6*diff(x(t),t)+10*x(t)=exp(-2*t)*cos(t),x(t), singsol=all)
 

\[ x \left (t \right ) = \left (c_{2} \sin \left (t \right )+\cos \left (t \right ) c_{1} \right ) {\mathrm e}^{-3 t}+\frac {{\mathrm e}^{-2 t} \left (\cos \left (t \right )+2 \sin \left (t \right )\right )}{5} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 47

DSolve[D[x[t],{t,2}]+6*D[x[t],t]+10*x[t]==Exp[-3*t]*Cos[t],x[t],t,IncludeSingularSolutions -> True]
 

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