72.18.4 problem 4

Internal problem ID [14957]
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 : 4
Date solved : Tuesday, January 28, 2025 at 07:25:28 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

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

\[ y = \frac {\left (8 c_{2} +6 t \right ) \sin \left (2 t \right )}{8}+\frac {\left (8 c_{1} +3\right ) \cos \left (2 t \right )}{8} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 64

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

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