Internal problem ID [12902]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 4. Forcing and Resonance. Section 4.3 page 424
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=2 \cos \left (3 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(t),t$2)+9*y(t)=2*cos(3*t),y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (3 t \right ) c_{2} +\cos \left (3 t \right ) c_{1} +\frac {\cos \left (3 t \right )}{9}+\frac {\sin \left (3 t \right ) t}{3} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 31
DSolve[y''[t]+9*y[t]==2*Cos[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \left (\frac {1}{18}+c_1\right ) \cos (3 t)+\frac {1}{3} (t+3 c_2) \sin (3 t) \]