Internal problem ID [12888]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+20 y=-\cos \left (5 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(t),t$2)+4*diff(y(t),t)+20*y(t)=-cos(5*t),y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-2 t} \sin \left (4 t \right ) c_{2} +{\mathrm e}^{-2 t} \cos \left (4 t \right ) c_{1} +\frac {\cos \left (5 t \right )}{85}-\frac {4 \sin \left (5 t \right )}{85} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 45
DSolve[y''[t]+4*y'[t]+20*y[t]==-Cos[5*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{85} (\cos (5 t)-4 \sin (5 t))+c_2 e^{-2 t} \cos (4 t)+c_1 e^{-2 t} \sin (4 t) \]