Internal problem ID [7926]
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]
\[ \boxed {y^{\prime } \left (\sin \left (x \right )+1\right ) \sin \left (y\right )+\cos \left (x \right ) \left (\cos \left (y\right )-1\right )=0} \]
✓ Solution by Maple
Time used: 0.094 (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)
\[ y \left (x \right ) = \arccos \left (\sin \left (x \right ) c_{1} +c_{1} +1\right ) \]
✓ Solution by Mathematica
Time used: 3.427 (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 \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*}