Internal problem ID [7927]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 347.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \left (1+\sin \relax (x )\right ) \sin \relax (y)+\cos \relax (x ) \left (\cos \relax (y)-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.315 (sec). Leaf size: 12
dsolve(diff(y(x),x)*(1+sin(x))*sin(y(x))+cos(x)*(cos(y(x))-1) = 0,y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (c_{1} \sin \relax (x )+c_{1}+1\right ) \]
✓ Solution by Mathematica
Time used: 1.049 (sec). Leaf size: 37
DSolve[Cos[x]*(-1 + Cos[y[x]]) + (1 + Sin[x])*Sin[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to 2 \text {ArcSin}\left (\frac {1}{4} c_1 \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )\right ) \\ y(x)\to 0 \\ \end{align*}