Internal problem ID [14687]
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: 12.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime }=\sec \left (2 t \right ) \tan \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(y(t),t$3)+4*diff(y(t),t)=sec(2*t)*tan(2*t),y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\ln \left (\sec \left (2 t \right )\right ) \cos \left (2 t \right )}{8}+\frac {\left (1-4 c_{2} \right ) \cos \left (2 t \right )}{8}+\frac {\left (2 t +4 c_{1} \right ) \sin \left (2 t \right )}{8}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.241 (sec). Leaf size: 47
DSolve[y'''[t]+4*y'[t]==Sec[2*t]*Tan[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} \sin (2 t) \arctan (\tan (2 t))+\frac {1}{8} \cos (2 t) (\log (\cos (2 t))+1-4 c_2)+c_1 \sin (t) \cos (t)+c_3 \]