Internal problem ID [14178]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }-\frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.848 (sec). Leaf size: 45
DSolve[x'[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*}