74.12.7 problem 7

Internal problem ID [16314]
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 : 7
Date solved : Tuesday, January 28, 2025 at 09:03:01 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 37

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

\[ y(t)\to \left (-\frac {t}{4}+c_1\right ) \cos (4 t)+\frac {1}{16} \sin (4 t) (\log (\sin (4 t))+16 c_2) \]