7.12.17 problem 18

Internal problem ID [399]
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 : 18
Date solved : Wednesday, February 05, 2025 at 03:41:00 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+10 x^{\prime }+650 x&=100 \cos \left (\omega t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 74

dsolve(diff(x(t),t$2)+10*diff(x(t),t)+650*x(t)=100*cos(omega*t),x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\left (\omega ^{2}-50 \omega +650\right ) \left (\omega ^{2}+50 \omega +650\right ) \left (\sin \left (25 t \right ) c_2 +\cos \left (25 t \right ) c_1 \right ) {\mathrm e}^{-5 t}-100 \omega ^{2} \cos \left (\omega t \right )+1000 \omega \sin \left (\omega t \right )+65000 \cos \left (\omega t \right )}{\omega ^{4}-1200 \omega ^{2}+422500} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 62

DSolve[D[x[t],{t,2}]+10*D[x[t],t]+650*x[t]==100*Cos[w*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -\frac {100 \left (\left (w^2-650\right ) \cos (t w)-10 w \sin (t w)\right )}{w^4-1200 w^2+422500}+c_2 e^{-5 t} \cos (25 t)+c_1 e^{-5 t} \sin (25 t) \]