8.12.3 problem 3

Internal problem ID [910]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.6, Forced Oscillations and Resonance. Page 362
Problem number : 3
Date solved : Wednesday, February 05, 2025 at 04:44:16 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+100 x&=225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=375\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

dsolve([diff(x(t),t$2)+100*x(t)=225*cos(5*t)+300*sin(5*t),x(0) = 375, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = -2 \sin \left (10 t \right )+372 \cos \left (10 t \right )+3 \cos \left (5 t \right )+4 \sin \left (5 t \right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 30

DSolve[{D[x[t],{t,2}]+100*x[t]==225*Cos[5*t]+300*Sin[5*t],{x[0]==375,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 4 \sin (5 t)-2 \sin (10 t)+3 \cos (5 t)+372 \cos (10 t) \]