74.12.8 problem 8

Internal problem ID [16315]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 09:03:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+16 y&=\cot \left (4 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 35

dsolve(diff(y(t),t$2)+16*y(t)=cot(4*t),y(t), singsol=all)
 

\[ y = \sin \left (4 t \right ) c_{2} +\cos \left (4 t \right ) c_{1} +\frac {\sin \left (4 t \right ) \ln \left (\csc \left (4 t \right )-\cot \left (4 t \right )\right )}{16} \]

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 67

DSolve[D[y[t],{t,2}]+16*y[t]==Cot[4*t],y[t],t,IncludeSingularSolutions -> True]
 

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