72.17.5 problem 5

Internal problem ID [14941]
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
Date solved : Tuesday, January 28, 2025 at 07:21:28 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=\cos \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(t),t$2)+6*diff(y(t),t)+8*y(t)=cos(t),y(t), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{-4 t} c_{1}}{2}+\frac {7 \cos \left (t \right )}{85}+\frac {6 \sin \left (t \right )}{85}+{\mathrm e}^{-2 t} c_{2} \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 68

DSolve[D[y[t],{t,2}]+6*D[y[t],t]+8*y[t]==Cos[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (\int _1^t-\frac {1}{2} e^{4 K[1]} \cos (K[1])dK[1]+e^{2 t} \int _1^t\frac {1}{2} e^{2 K[2]} \cos (K[2])dK[2]+c_2 e^{2 t}+c_1\right ) \]