60.1.198 problem 199

Internal problem ID [10212]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 199
Date solved : Monday, January 27, 2025 at 06:38:52 PM
CAS classification : [_separable]

\begin{align*} \sin \left (2 x \right ) y^{\prime }+\sin \left (2 y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.412 (sec). Leaf size: 80

dsolve(sin(2*x)*diff(y(x),x) + sin(2*y(x))=0,y(x), singsol=all)
 

\[ y = \frac {\arctan \left (-\frac {2 \sin \left (2 x \right ) c_{1}}{\cos \left (2 x \right ) c_{1}^{2}-c_{1}^{2}-\cos \left (2 x \right )-1}, \frac {\cos \left (2 x \right ) c_{1}^{2}-c_{1}^{2}+\cos \left (2 x \right )+1}{\cos \left (2 x \right ) c_{1}^{2}-c_{1}^{2}-\cos \left (2 x \right )-1}\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.444 (sec). Leaf size: 68

DSolve[Sin[2*x]*D[y[x],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*}