74.12.36 problem 36

Internal problem ID [16343]
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 : 36
Date solved : Tuesday, January 28, 2025 at 09:05:44 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+16 y&=\tan \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 56

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

\[ y = \frac {\sin \left (2 t \right ) \cos \left (2 t \right ) \ln \left (\cos \left (2 t \right )\right )}{4}+\frac {\left (-t +4 c_{1} \right ) \cos \left (2 t \right )^{2}}{2}+\frac {\sin \left (2 t \right ) \left (16 c_{2} -1\right ) \cos \left (2 t \right )}{8}+\frac {t}{4}-c_{1} \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 61

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

\[ y(t)\to \cos (4 t) \int _1^t-\frac {1}{2} \sin ^2(2 K[1])dK[1]+c_1 \cos (4 t)-\frac {1}{16} \sin (4 t) (\cos (4 t)-2 \log (\cos (2 t))+1-16 c_2) \]