44.6.21 problem 21

Internal problem ID [7165]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 21
Date solved : Tuesday, February 04, 2025 at 12:43:17 AM
CAS classification : [_linear]

\begin{align*} r^{\prime }+r \sec \left (t \right )&=\cos \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 28

dsolve(diff(r(t),t)+r(t)*sec(t)=cos(t),r(t), singsol=all)
 

\[ r = \frac {\left (t -\cos \left (t \right )+c_1 \right ) \left (\cos \left (t \right )-\sin \left (t \right )+1\right )}{\cos \left (t \right )+1+\sin \left (t \right )} \]

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 25

DSolve[D[r[t],t]+r[t]*Sec[t]==Cos[t],r[t],t,IncludeSingularSolutions -> True]
 

\[ r(t)\to e^{-2 \text {arctanh}\left (\tan \left (\frac {t}{2}\right )\right )} (t-\cos (t)+c_1) \]