7.12.13 problem 14

Internal problem ID [395]
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 : 14
Date solved : Wednesday, February 05, 2025 at 03:38:51 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+8 x^{\prime }+25 x&=200 \cos \left (t \right )+520 \sin \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=-30\\ x^{\prime }\left (0\right )&=-10 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 29

dsolve([diff(x(t),t$2)+8*diff(x(t),t)+25*x(t)=200*cos(t)+520*sin(t),x(0) = -30, D(x)(0) = -10],x(t), singsol=all)
 

\[ x \left (t \right ) = \left (-31 \cos \left (3 t \right )-52 \sin \left (3 t \right )\right ) {\mathrm e}^{-4 t}+\cos \left (t \right )+22 \sin \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 34

DSolve[{D[x[t],{t,2}]+8*D[x[t],t]+25*x[t]==200*Cos[t]+520*Sin[t],{x[0]==-30,Derivative[1][x][0] ==-10}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 22 \sin (t)-52 e^{-4 t} \sin (3 t)+\cos (t)-31 e^{-4 t} \cos (3 t) \]