Internal problem ID [14692]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime }=\sec \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 97
dsolve(diff(y(t),t$3)+4*diff(y(t),t)=sec(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {i \left ({\mathrm e}^{2 i t}-{\mathrm e}^{-2 i t}\right ) \ln \left (\frac {{\mathrm e}^{2 i t}}{{\mathrm e}^{4 i t}+1}\right )}{16}-\frac {i \arctan \left ({\mathrm e}^{2 i t}\right )}{4}+\frac {i \left (-1-\ln \left (2\right )\right ) {\mathrm e}^{-2 i t}}{16}+\frac {i \left (1+\ln \left (2\right )\right ) {\mathrm e}^{2 i t}}{16}+\frac {\left (-t -2 c_{2} \right ) \cos \left (2 t \right )}{4}+\frac {\left (4 c_{1} +1\right ) \sin \left (2 t \right )}{8}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.118 (sec). Leaf size: 63
DSolve[y'''[t]+4*y'[t]==Sec[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} \left (-2 t \cos (2 t)-8 c_2 \cos ^2(t)+4 c_1 \sin (2 t)-\log (\cos (t)-\sin (t))+\log (\sin (t)+\cos (t))+\sin (2 t) \log (\cos (2 t))+8 c_3\right ) \]