65.6.10 problem 12.1 (x)

Internal problem ID [13759]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number : 12.1 (x)
Date solved : Tuesday, January 28, 2025 at 06:02:08 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+6 x^{\prime }+10 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=3\\ x^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 18

dsolve([diff(x(t),t$2)+6*diff(x(t),t)+10*x(t)=0,x(0) = 3, D(x)(0) = 1],x(t), singsol=all)
 

\[ x \left (t \right ) = {\mathrm e}^{-3 t} \left (10 \sin \left (t \right )+3 \cos \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

DSolve[{D[x[t],{t,2}]+6*D[x[t],t]+10*x[t]==0,{x[0]==3,Derivative[1][x][0 ]==1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-3 t} (10 \sin (t)+3 \cos (t)) \]