Internal problem ID [13216]
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 4.2 page 412
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+20 y=3+2 \cos \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(t),t$2)+4*diff(y(t),t)+20*y(t)=3+2*cos(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (4 t \right ) {\mathrm e}^{-2 t} c_{2} +\cos \left (4 t \right ) {\mathrm e}^{-2 t} c_{1} +\frac {3}{20}+\frac {\sin \left (2 t \right )}{20}+\frac {\cos \left (2 t \right )}{10} \]
✓ Solution by Mathematica
Time used: 1.265 (sec). Leaf size: 47
DSolve[y''[t]+4*y'[t]+20*y[t]==3+2*Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{20} \left (\sin (2 t)+2 \cos (2 t)+20 c_2 e^{-2 t} \cos (4 t)+20 c_1 e^{-2 t} \sin (4 t)+3\right ) \]