Internal problem ID [10458]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 2, Second order linear equations. Section 2.3.2 Resonance Exercises page
114
Problem number: 7(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+w^{2} x-\cos \left (\beta t \right )=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 27
dsolve([diff(x(t),t$2)+w^2*x(t)=cos(beta*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\cos \left (t w \right )-\cos \left (\beta t \right )}{\beta ^{2}-w^{2}} \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 28
DSolve[{x''[t]+w^2*x[t]==Cos[\[Beta]*t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {\cos (\beta t)-\cos (t w)}{w^2-\beta ^2} \\ \end{align*}