Internal problem ID [14690]
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: 15.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+9 y^{\prime }=\sec \left (3 t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 132
dsolve(diff(y(t),t$3)+9*diff(y(t),t)=sec(3*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {i \left ({\mathrm e}^{3 i t}-{\mathrm e}^{-3 i t}\right ) \ln \left (\frac {{\mathrm e}^{3 i t}}{{\mathrm e}^{6 i t}+1}\right )}{54}-\frac {i \arctan \left (2 \,{\mathrm e}^{i t}-\sqrt {3}\right )}{27}-\frac {i \arctan \left (2 \,{\mathrm e}^{i t}+\sqrt {3}\right )}{27}-\frac {i \arctan \left ({\mathrm e}^{3 i t}\right )}{27}-\frac {i {\mathrm e}^{-3 i t}}{54}+\frac {i {\mathrm e}^{3 i t}}{54}+\frac {i \arctan \left ({\mathrm e}^{i t}\right )}{27}+\frac {\left (1+9 c_{1} -\ln \left (2\right )\right ) \sin \left (3 t \right )}{27}+\frac {\left (-t -3 c_{2} \right ) \cos \left (3 t \right )}{9}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.245 (sec). Leaf size: 73
DSolve[y'''[t]+9*y'[t]==Sec[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{27} \left (-3 (t+3 c_2) \cos (3 t)-\log \left (\cos \left (\frac {3 t}{2}\right )-\sin \left (\frac {3 t}{2}\right )\right )+\log \left (\sin \left (\frac {3 t}{2}\right )+\cos \left (\frac {3 t}{2}\right )\right )+\sin (3 t) (\log (\cos (3 t))+9 c_1)+27 c_3\right ) \]