72.17.8 problem 8

Internal problem ID [14944]
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
Date solved : Tuesday, January 28, 2025 at 07:22:10 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=-\cos \left (5 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = \sin \left (4 t \right ) {\mathrm e}^{-2 t} c_{2} +\cos \left (4 t \right ) {\mathrm e}^{-2 t} c_{1} +\frac {\cos \left (5 t \right )}{85}-\frac {4 \sin \left (5 t \right )}{85} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 45

DSolve[D[y[t],{t,2}]+4*D[y[t],t]+20*y[t]==-Cos[5*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{85} (\cos (5 t)-4 \sin (5 t))+c_2 e^{-2 t} \cos (4 t)+c_1 e^{-2 t} \sin (4 t) \]