Internal problem ID [10113]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 9. Variables
searated or separable. Page 13
Problem number: Ex 1.
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: 0.0 (sec). Leaf size: 11
dsolve((sec(x)*cos(y(x))^2)-(cos(x)*sin(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {1}{\tan \relax (x )+c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 0.867 (sec). Leaf size: 45
DSolve[(Sec[x]*Cos[y[x]]^2)-(Cos[x]*Sin[y[x]])*y'[x]==0,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*}