8.12.7 problem 8

Internal problem ID [914]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number : 8
Date solved : Wednesday, February 05, 2025 at 04:44:29 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+3 x^{\prime }+5 x&=-4 \cos \left (5 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 43

dsolve(diff(x(t),t$2)+3*diff(x(t),t)+5*x(t)=-4*cos(5*t),x(t), singsol=all)
 

\[ x \left (t \right ) = {\mathrm e}^{-\frac {3 t}{2}} \sin \left (\frac {\sqrt {11}\, t}{2}\right ) c_2 +{\mathrm e}^{-\frac {3 t}{2}} \cos \left (\frac {\sqrt {11}\, t}{2}\right ) c_1 +\frac {16 \cos \left (5 t \right )}{125}-\frac {12 \sin \left (5 t \right )}{125} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 65

DSolve[D[x[t],{t,2}]+3*D[x[t],t]+5*x[t]==-4*Cos[5*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {4}{125} (4 \cos (5 t)-3 \sin (5 t))+c_2 e^{-3 t/2} \cos \left (\frac {\sqrt {11} t}{2}\right )+c_1 e^{-3 t/2} \sin \left (\frac {\sqrt {11} t}{2}\right ) \]