74.12.38 problem 38

Internal problem ID [16345]
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 : 38
Date solved : Tuesday, January 28, 2025 at 09:05:57 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\sec \left (3 t \right ) \tan \left (3 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 38

dsolve(diff(y(t),t$2)+9*y(t)=sec(3*t)*tan(3*t),y(t), singsol=all)
 

\[ y = \frac {\ln \left (\sec \left (3 t \right )\right ) \sin \left (3 t \right )}{9}+\frac {\left (9 c_{2} -1\right ) \sin \left (3 t \right )}{9}+\frac {\cos \left (3 t \right ) \left (t +3 c_{1} \right )}{3} \]

✓ Solution by Mathematica

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

DSolve[D[y[t],{t,2}]+9*y[t]==Sec[3*t]*Tan[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{9} (\cos (3 t) \arctan (\tan (3 t))+9 c_1 \cos (3 t)+\sin (3 t) (-\log (\cos (3 t))-1+9 c_2)) \]