74.12.39 problem 39

Internal problem ID [16346]
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 : 39
Date solved : Tuesday, January 28, 2025 at 09:06:02 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 38

dsolve(diff(y(t),t$2)+4*y(t)=sec(2*t)*tan(2*t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 46

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

\[ y(t)\to \frac {1}{4} (\cos (2 t) \arctan (\tan (2 t))+4 c_1 \cos (2 t)+\sin (2 t) (-\log (\cos (2 t))-1+4 c_2)) \]