Internal problem ID [10686]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 14, Inhomogeneous second order linear equations. Exercises page 140
Problem number: 14.1 (vi).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+\omega ^{2} x-\sin \left (\alpha t \right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(diff(x(t),t$2)+omega^2*x(t)=sin(alpha*t),x(t), singsol=all)
\[ x \left (t \right ) = \sin \left (t \omega \right ) c_{2} +\cos \left (t \omega \right ) c_{1} -\frac {\sin \left (\alpha t \right )}{\alpha ^{2}-\omega ^{2}} \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 37
DSolve[x''[t]+w^2*x[t]==Sin[a*t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {\sin (a t)}{a^2-w^2}+c_1 \cos (t w)+c_2 \sin (t w) \\ \end{align*}