74.21.9 problem 24

Internal problem ID [16647]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 5. Applications of Higher Order Equations. Exercises 5.3, page 249
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 09:14:57 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+\frac {x^{\prime }}{10}+x&=3 \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: 0.054 (sec). Leaf size: 46

dsolve([diff(x(t),t$2)+1/10*diff(x(t),t)+x(t)=3*cos(2*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = -\frac {125 \,{\mathrm e}^{-\frac {t}{20}} \sqrt {399}\, \sin \left (\frac {\sqrt {399}\, t}{20}\right )}{30058}+\frac {225 \,{\mathrm e}^{-\frac {t}{20}} \cos \left (\frac {\sqrt {399}\, t}{20}\right )}{226}+\frac {15 \sin \left (2 t \right )}{226}-\frac {225 \cos \left (2 t \right )}{226} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 74

DSolve[{D[x[t],{t,2}]+1/10*D[x[t],t]+x[t]==3*Cos[2*t],{x[0]==0,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -\frac {5 e^{-t/20} \left (-399 e^{t/20} \sin (2 t)+25 \sqrt {399} \sin \left (\frac {\sqrt {399} t}{20}\right )+5985 e^{t/20} \cos (2 t)-5985 \cos \left (\frac {\sqrt {399} t}{20}\right )\right )}{30058} \]