74.14.17 problem 17

Internal problem ID [16422]
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
Date solved : Tuesday, January 28, 2025 at 09:07:47 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=\sec \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 86

dsolve(diff(y(t),t$3)+4*diff(y(t),t)=sec(2*t),y(t), singsol=all)
 

\[ y = \frac {i \left ({\mathrm e}^{2 i t}-{\mathrm e}^{-2 i t}\right ) \ln \left (\frac {{\mathrm e}^{2 i t}}{{\mathrm e}^{4 i t}+1}\right )}{16}-\frac {i \arctan \left ({\mathrm e}^{2 i t}\right )}{4}+\frac {i \left (-1-\ln \left (2\right )\right ) {\mathrm e}^{-2 i t}}{16}+\frac {i \left (1+\ln \left (2\right )\right ) {\mathrm e}^{2 i t}}{16}+\frac {\left (-t -2 c_{2} \right ) \cos \left (2 t \right )}{4}+\frac {\left (4 c_{1} +1\right ) \sin \left (2 t \right )}{8}+c_{3} \]

✓ Solution by Mathematica

Time used: 60.044 (sec). Leaf size: 49

DSolve[D[ y[t],{t,3}]+4*D[y[t],t]==Sec[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^t\left (\cos (2 K[1]) \left (c_1+\frac {1}{4} \log (\cos (2 K[1]))\right )+\cos (K[1]) (2 c_2+K[1]) \sin (K[1])\right )dK[1]+c_3 \]