Internal problem ID [8694]
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]
\[ \boxed {y^{\prime } \sin \left (y\right ) \cos \left (x \right )+\cos \left (y\right ) \sin \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 9
dsolve(diff(y(x),x)*sin(y(x))*cos(x)+cos(y(x))*sin(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \arccos \left (c_{1} \sec \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 6.074 (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 -\arccos \left (\frac {1}{2} c_1 \sec (x)\right ) \\ y(x)\to \arccos \left (\frac {1}{2} c_1 \sec (x)\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}