68.14.17 problem 17

Internal problem ID [17709]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 17
Date solved : Thursday, October 02, 2025 at 02:27:15 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 59

ode:=diff(diff(diff(y(t),t),t),t)+4*diff(y(t),t) = sec(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {i \arctan \left ({\mathrm e}^{2 i t}\right )}{4}+c_3 +\frac {{\mathrm e}^{-2 i t} \left (-i \ln \left (\sec \left (2 t \right )\right )+4 i c_1 -4 c_2 -2 t \right )}{16}+\frac {{\mathrm e}^{2 i t} \left (i \ln \left (\sec \left (2 t \right )\right )-4 i c_1 -4 c_2 -2 t \right )}{16} \]

✓ Mathematica. Time used: 60.027 (sec). Leaf size: 49

ode=D[ y[t],{t,3}]+4*D[y[t],t]==Sec[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \int _1^t\left (\cos (2 K[1]) \left (c_1+\frac {1}{4} \log (\cos (2 K[1]))\right )+\cos (K[1]) (2 c_2+K[1]) \sin (K[1])\right )dK[1]+c_3 \end{align*}

✓ Sympy. Time used: 0.369 (sec). Leaf size: 49

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*Derivative(y(t), t) + Derivative(y(t), (t, 3)) - 1/cos(2*t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} + \left (C_{2} - \frac {t}{4}\right ) \cos {\left (2 t \right )} + \left (C_{3} + \frac {\log {\left (\cos {\left (2 t \right )} \right )}}{8}\right ) \sin {\left (2 t \right )} - \frac {\log {\left (\sin {\left (2 t \right )} - 1 \right )}}{16} + \frac {\log {\left (\sin {\left (2 t \right )} + 1 \right )}}{16} \]