74.12.33 problem 33

Internal problem ID [16269]
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 : 33
Date solved : Monday, March 31, 2025 at 02:48:57 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=diff(diff(y(t),t),t)+9*y(t) = sec(3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {\ln \left (\sec \left (3 t \right )\right ) \cos \left (3 t \right )}{9}+\cos \left (3 t \right ) c_1 +\frac {\sin \left (3 t \right ) \left (t +3 c_2 \right )}{3} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 37

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

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

✓ Sympy. Time used: 0.242 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*y(t) + Derivative(y(t), (t, 2)) - 1/cos(3*t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} + \frac {t}{3}\right ) \sin {\left (3 t \right )} + \left (C_{2} + \frac {\log {\left (\cos {\left (3 t \right )} \right )}}{9}\right ) \cos {\left (3 t \right )} \]