Internal problem ID [7938]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 358.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \sin \relax (y) \cos \relax (x )+\cos \relax (y) \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.218 (sec). Leaf size: 11
dsolve(diff(y(x),x)*sin(y(x))*cos(x)+cos(y(x))*sin(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {c_{1}}{\cos \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 2.361 (sec). Leaf size: 47
DSolve[Cos[y[x]]*Sin[x] + Cos[x]*Sin[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcCos}\left (\frac {1}{2} c_1 \sec (x)\right ) \\ y(x)\to \text {ArcCos}\left (\frac {1}{2} c_1 \sec (x)\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}