Internal problem ID [11714]
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]]
\[ \boxed {x^{\prime \prime }+\omega ^{2} x=\sin \left (\alpha t \right )} \]
✓ 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: 0.359 (sec). Leaf size: 56
DSolve[x''[t]+w^2*x[t]==Sin[a*t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {-\left (c_1 \left (a^2-w^2\right ) \cos (t w)\right )+c_2 \left (w^2-a^2\right ) \sin (t w)+\sin (a t)}{(w-a) (a+w)} \]