74.21.7 problem 22 (a)

Internal problem ID [16645]
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 : 22 (a)
Date solved : Tuesday, January 28, 2025 at 09:14:39 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+x&=\cos \left (\frac {9 t}{10}\right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.100 (sec). Leaf size: 17

dsolve([diff(x(t),t$2)+x(t)=cos(9/10*t),x(0) = 0, D(x)(0) = 1],x(t), singsol=all)
 

\[ x \left (t \right ) = \sin \left (t \right )-\frac {100 \cos \left (t \right )}{19}+\frac {100 \cos \left (\frac {9 t}{10}\right )}{19} \]

✓ Solution by Mathematica

Time used: 0.127 (sec). Leaf size: 96

DSolve[{D[x[t],{t,2}]+x[t]==Cos[9/10*t],{x[0]==0,Derivative[1][x][0 ]==1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \sin (t) \left (-\int _1^0\cos \left (\frac {9 K[2]}{10}\right ) \cos (K[2])dK[2]\right )+\sin (t) \int _1^t\cos \left (\frac {9 K[2]}{10}\right ) \cos (K[2])dK[2]-\cos (t) \int _1^0-\cos \left (\frac {9 K[1]}{10}\right ) \sin (K[1])dK[1]+\cos (t) \int _1^t-\cos \left (\frac {9 K[1]}{10}\right ) \sin (K[1])dK[1]+\sin (t) \]