72.18.5 problem 5

Internal problem ID [14958]
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 4.3 page 424
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 07:25:32 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=2 \cos \left (3 t \right ) \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(t),t$2)+9*y(t)=2*cos(3*t),y(t), singsol=all)
 

\[ y = \frac {\left (9 c_{1} +1\right ) \cos \left (3 t \right )}{9}+\frac {\sin \left (3 t \right ) \left (t +3 c_{2} \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 64

DSolve[D[y[t],{t,2}]+9*y[t]==2*Cos[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sin (3 t) \int _1^t\frac {2}{3} \cos ^2(3 K[2])dK[2]+\cos (3 t) \int _1^t-\frac {1}{3} \sin (6 K[1])dK[1]+c_1 \cos (3 t)+c_2 \sin (3 t) \]