72.18.2 problem 2

Internal problem ID [14955]
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 : 2
Date solved : Tuesday, January 28, 2025 at 07:25:21 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=5 \sin \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(diff(y(t),t$2)+9*y(t)=5*sin(2*t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 24

DSolve[D[y[t],{t,2}]+9*y[t]==5*Sin[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sin (2 t)+c_1 \cos (3 t)+c_2 \sin (3 t) \]