Internal problem ID [2875]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 126.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+\csc \left (2 x \right ) \sin \left (2 y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.237 (sec). Leaf size: 105
dsolve(diff(y(x),x)+csc(2*x)*sin(2*y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\arctan \left (-\frac {2 c_{1} \left (\sin \left (4 x \right )+2 \sin \left (2 x \right )\right )}{c_{1}^{2} \cos \left (4 x \right )-c_{1}^{2}-\cos \left (4 x \right )-4 \cos \left (2 x \right )-3}, \frac {c_{1}^{2} \cos \left (4 x \right )-c_{1}^{2}+\cos \left (4 x \right )+4 \cos \left (2 x \right )+3}{c_{1}^{2} \cos \left (4 x \right )-c_{1}^{2}-\cos \left (4 x \right )-4 \cos \left (2 x \right )-3}\right )}{2} \]
✓ Solution by Mathematica
Time used: 4.607 (sec). Leaf size: 85
DSolve[y'[x]+Csc[2 x] Sin[2 y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcTan}\left (e^{2 c_1} \cot (x)\right ) \\ y(x)\to 0 \\ y(x)\to \frac {1}{2} \pi (-1)^{\left \lfloor \frac {1}{2}-\frac {\arg (\cot (x))}{\pi }\right \rfloor } \\ y(x)\to \frac {1}{2} \pi \left ((-1)^{\left \lfloor \frac {\arg (\cot (x))}{\pi }+\frac {1}{2}\right \rfloor }-(-1)^{\left \lfloor \frac {1}{2}-\frac {\arg (\tan (x))}{\pi }\right \rfloor }\right ) \\ \end{align*}