63.10.1 problem 6

Internal problem ID [13151]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.3.2 Resonance Exercises page 114
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 05:09:28 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x&=\cos \left (2 t \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 27

dsolve([diff(x(t),t$2)+1/100*diff(x(t),t)+4*x(t)=cos(2*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {20000 \,{\mathrm e}^{-\frac {t}{200}} \sqrt {159999}\, \sin \left (\frac {\sqrt {159999}\, t}{200}\right )}{159999}+50 \sin \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 7.503 (sec). Leaf size: 37

DSolve[{D[x[t],{t,2}]+1/100*D[x[t],t]+4*x[t]==Cos[2*t],{x[0]==0,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 50 \sin (2 t)-\frac {20000 e^{-t/200} \sin \left (\frac {\sqrt {159999} t}{200}\right )}{\sqrt {159999}} \]