74.14.16 problem 16

Internal problem ID [16421]
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 : 16
Date solved : Tuesday, January 28, 2025 at 09:07:46 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 1.348 (sec). Leaf size: 63

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

\[ y(t)\to -\frac {\arctan (\tan (t)) (t \sin (t)+\cos (t))}{t}-2 (1+c_2) \cos ^2\left (\frac {t}{2}\right )-\cos (t) \log (\cos (t))+c_1 \sin (t)-\frac {2 \cos (t) \log (\cos (t))}{\log \left (\sec ^2(t)\right )}+c_3 \]