74.4.20 problem 20

Internal problem ID [15913]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 08:19:49 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=\frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 11

dsolve(diff(x(t),t)=sec(t)^2/(sec(x(t))*tan(x(t))),x(t), singsol=all)
 

\[ x \left (t \right ) = \arccos \left (\frac {1}{\tan \left (t \right )+c_{1}}\right ) \]

✓ Solution by Mathematica

Time used: 0.763 (sec). Leaf size: 45

DSolve[D[x[t],t]==Sec[t]^2/(Sec[x[t]]*Tan[x[t]]),x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -\sec ^{-1}(\tan (t)+2 c_1) \\ x(t)\to \sec ^{-1}(\tan (t)+2 c_1) \\ x(t)\to -\frac {\pi }{2} \\ x(t)\to \frac {\pi }{2} \\ \end{align*}