8.12.6 problem 7

Internal problem ID [913]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number : 7
Date solved : Monday, January 27, 2025 at 03:18:43 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+4 x^{\prime }+4 x&=10 \cos \left (3 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(x(t),t$2)+4*diff(x(t),t)+4*x(t)=10*cos(3*t),x(t), singsol=all)
 

\[ x \left (t \right ) = \left (c_1 t +c_2 \right ) {\mathrm e}^{-2 t}-\frac {50 \cos \left (3 t \right )}{169}+\frac {120 \sin \left (3 t \right )}{169} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 35

DSolve[D[x[t],{t,2}]+4*D[x[t],t]+4*x[t]==10*Cos[3*t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {120}{169} \sin (3 t)-\frac {50}{169} \cos (3 t)+e^{-2 t} (c_2 t+c_1) \]