8.12.4 problem 4

Internal problem ID [911]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number : 4
Date solved : Wednesday, February 05, 2025 at 04:44:22 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+25 x&=90 \cos \left (4 t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=90 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve([diff(x(t),t$2)+25*x(t)=90*cos(4*t),x(0) = 0, D(x)(0) = 90],x(t), singsol=all)
 

\[ x \left (t \right ) = 18 \sin \left (5 t \right )-10 \cos \left (5 t \right )+10 \cos \left (4 t \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 26

DSolve[{D[x[t],{t,2}]+25*x[t]==90*Cos[4*t],{x[0]==0,Derivative[1][x][0 ]==90}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 2 (9 \sin (5 t)+5 \cos (4 t)-5 \cos (5 t)) \]