Internal problem ID [14691]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime }=-\sec \left (t \right ) \tan \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(t),t$3)+diff(y(t),t)=-sec(t)*tan(t),y(t), singsol=all)
\[ y \left (t \right ) = \cos \left (t \right ) \ln \left (\sec \left (t \right )\right )+\left (-c_{2} -1\right ) \cos \left (t \right )+\left (-t +c_{1} \right ) \sin \left (t \right )+c_{3} \]
✓ Solution by Mathematica
Time used: 0.141 (sec). Leaf size: 31
DSolve[y'''[t]+y'[t]==-Sec[t]*Tan[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\sin (t) \arctan (\tan (t))+c_1 \sin (t)-\cos (t) (\log (\cos (t))+1+c_2)+c_3 \]