Internal problem ID [8535]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 199.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sin \left (2 x \right ) y^{\prime }+\sin \left (2 y\right )=0} \]
✓ Solution by Maple
Time used: 0.485 (sec). Leaf size: 80
dsolve(sin(2*x)*diff(y(x),x) + sin(2*y(x))=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\arctan \left (-\frac {2 \sin \left (2 x \right ) c_{1}}{\cos \left (2 x \right ) c_{1}^{2}-c_{1}^{2}-\cos \left (2 x \right )-1}, \frac {\cos \left (2 x \right ) c_{1}^{2}-c_{1}^{2}+\cos \left (2 x \right )+1}{\cos \left (2 x \right ) c_{1}^{2}-c_{1}^{2}-\cos \left (2 x \right )-1}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.462 (sec). Leaf size: 68
DSolve[Sin[2*x]*y'[x] + Sin[2*y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \arccos (-\tanh (\text {arctanh}(\cos (2 x))+2 c_1)) \\ y(x)\to \frac {1}{2} \arccos (-\tanh (\text {arctanh}(\cos (2 x))+2 c_1)) \\ y(x)\to 0 \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}