Internal problem ID [12042]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 15, Resonance. Exercises page 148
Problem number: 15.1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+\omega ^{2} x=\cos \left (\alpha t \right )} \] With initial conditions \begin {align*} [x \left (0\right ) = 0, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve([diff(x(t),t$2)+omega^2*x(t)=cos(alpha*t),x(0) = 0, D(x)(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\cos \left (\omega t \right )-\cos \left (\alpha t \right )}{\alpha ^{2}-\omega ^{2}} \]
✓ Solution by Mathematica
Time used: 0.25 (sec). Leaf size: 28
DSolve[{x''[t]+w^2*x[t]==Cos[a*t],{x[0]==0,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {\cos (t w)-\cos (a t)}{a^2-w^2} \]