72.17.10 problem 10

Internal problem ID [14946]
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 : 10
Date solved : Tuesday, January 28, 2025 at 07:23:45 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

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

\[ y = \left (c_{1} t +c_{2} \right ) {\mathrm e}^{-t}-\frac {2 \cos \left (3 t \right )}{25}+\frac {3 \sin \left (3 t \right )}{50} \]

✓ Solution by Mathematica

Time used: 0.180 (sec). Leaf size: 57

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

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