Internal problem ID [12897]
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: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+20 y={\mathrm e}^{-t} \cos \left (t \right )} \]
✓ 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)=exp(-t)*cos(t),y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-2 t} \sin \left (4 t \right ) c_{2} +{\mathrm e}^{-2 t} \cos \left (4 t \right ) c_{1} +\frac {{\mathrm e}^{-t} \left (\sin \left (t \right )+8 \cos \left (t \right )\right )}{130} \]
✓ Solution by Mathematica
Time used: 0.457 (sec). Leaf size: 44
DSolve[y''[t]+4*y'[t]+20*y[t]==Exp[-t]*Cos[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{130} e^{-2 t} \left (e^t \sin (t)+8 e^t \cos (t)+130 c_2 \cos (4 t)+130 c_1 \sin (4 t)\right ) \]