8.12.1 problem 1

Internal problem ID [908]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number : 1
Date solved : Wednesday, February 05, 2025 at 04:44:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+9 x&=10 \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: 0.018 (sec). Leaf size: 22

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

\[ x \left (t \right ) = -8 \cos \left (t \right )^{3}+6 \cos \left (t \right )+4 \cos \left (t \right )^{2}-2 \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 18

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

\[ x(t)\to 2 (\cos (2 t)-\cos (3 t)) \]