8.12.13 problem 13

Internal problem ID [920]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number : 13
Date solved : Wednesday, February 05, 2025 at 04:47:51 AM
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*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 45

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

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