72.17.16 problem 18

Internal problem ID [14952]
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 : 18
Date solved : Tuesday, January 28, 2025 at 07:24:39 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+20 y&=3+2 \cos \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 38

dsolve(diff(y(t),t$2)+4*diff(y(t),t)+20*y(t)=3+2*cos(2*t),y(t), singsol=all)
 

\[ y = \sin \left (4 t \right ) {\mathrm e}^{-2 t} c_{2} +\cos \left (4 t \right ) {\mathrm e}^{-2 t} c_{1} +\frac {3}{20}+\frac {\cos \left (2 t \right )}{10}+\frac {\sin \left (2 t \right )}{20} \]

✓ Solution by Mathematica

Time used: 0.636 (sec). Leaf size: 98

DSolve[D[y[t],{t,2}]+4*D[y[t],t]+20*y[t]==3+2*Cos[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-2 t} \left (\cos (4 t) \int _1^t-\frac {1}{4} e^{2 K[2]} (2 \cos (2 K[2])+3) \sin (4 K[2])dK[2]+\sin (4 t) \int _1^t\frac {1}{4} e^{2 K[1]} (2 \cos (2 K[1])+3) \cos (4 K[1])dK[1]+c_2 \cos (4 t)+c_1 \sin (4 t)\right ) \]