59.6.10 problem 12.1 (x)

Internal problem ID [15040]
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 : Thursday, October 02, 2025 at 10:02:16 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*}

✓ Maple. Time used: 0.064 (sec). Leaf size: 18

ode:=diff(diff(x(t),t),t)+6*diff(x(t),t)+10*x(t) = 0; 
ic:=[x(0) = 3, D(x)(0) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 20

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

\begin{align*} x(t)&\to e^{-3 t} (10 \sin (t)+3 \cos (t)) \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(10*x(t) + 6*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 3, Subs(Derivative(x(t), t), t, 0): 1} 
dsolve(ode,func=x(t),ics=ics)
 

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