7.12.12 problem 13

Internal problem ID [394]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.6 (Forced oscillations and resonance). Problems at page 171
Problem number : 13
Date solved : Saturday, March 29, 2025 at 04:52:40 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+2 x^{\prime }+26 x&=600 \cos \left (10 t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=10\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 36

ode:=diff(diff(x(t),t),t)+2*diff(x(t),t)+26*x(t) = 600*cos(10*t); 
ic:=x(0) = 10, D(x)(0) = 0; 
dsolve([ode,ic],x(t), singsol=all);
 

\[ x = \frac {\left (25790 \cos \left (5 t \right )-842 \sin \left (5 t \right )\right ) {\mathrm e}^{-t}}{1469}-\frac {11100 \cos \left (10 t \right )}{1469}+\frac {3000 \sin \left (10 t \right )}{1469} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 45

ode=D[x[t],{t,2}]+2*D[x[t],t]+26*x[t]==600*Cos[10*t]; 
ic={x[0]==10,Derivative[1][x][0] ==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to -\frac {2 e^{-t} \left (421 \sin (5 t)-1500 e^t \sin (10 t)-12895 \cos (5 t)+5550 e^t \cos (10 t)\right )}{1469} \]

✓ Sympy. Time used: 0.270 (sec). Leaf size: 39

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(26*x(t) - 600*cos(10*t) + 2*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 10, Subs(Derivative(x(t), t), t, 0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (- \frac {842 \sin {\left (5 t \right )}}{1469} + \frac {25790 \cos {\left (5 t \right )}}{1469}\right ) e^{- t} + \frac {3000 \sin {\left (10 t \right )}}{1469} - \frac {11100 \cos {\left (10 t \right )}}{1469} \]