74.12.32 problem 32

Internal problem ID [16339]
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 : 32
Date solved : Tuesday, January 28, 2025 at 09:05:19 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\tan \left (3 t \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

Time used: 0.234 (sec). Leaf size: 71

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

\[ y(t)\to \cos (3 t) \int _1^t-\frac {1}{3} \sin (3 K[1]) \tan ^2(3 K[1])dK[1]+\frac {1}{9} \sin (3 t) \text {arctanh}(\sin (3 t))-\frac {1}{9} \sin ^2(3 t)+c_1 \cos (3 t)+c_2 \sin (3 t) \]