Internal problem ID [12885]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+8 y=\cos \left (t \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(y(t),t$2)+6*diff(y(t),t)+8*y(t)=cos(t),y(t), singsol=all)
\[ y \left (t \right ) = -\frac {c_{1} {\mathrm e}^{-4 t}}{2}+\frac {7 \cos \left (t \right )}{85}+\frac {6 \sin \left (t \right )}{85}+c_{2} {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 35
DSolve[y''[t]+6*y'[t]+8*y[t]==Cos[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {6 \sin (t)}{85}+\frac {7 \cos (t)}{85}+e^{-4 t} \left (c_2 e^{2 t}+c_1\right ) \]