Internal problem ID [1884]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sec \relax (x ) \left (\cos ^{2}\relax (y)\right )-\cos \relax (x ) \sin \relax (y) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 11
dsolve(sec(x)*cos(y(x))^2=cos(x)*sin(y(x))*diff(y(x),x),y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {1}{\tan \relax (x )+c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 0.779 (sec). Leaf size: 45
DSolve[Sec[x]*Cos[y[x]]^2==Cos[x]*Sin[y[x]]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}(\tan (x)+2 c_1) \\ y(x)\to \sec ^{-1}(\tan (x)+2 c_1) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}