29.5.4 problem 119

Internal problem ID [4721]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 119
Date solved : Monday, January 27, 2025 at 09:34:01 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

\[ y \left (x \right ) = \frac {\arccos \left (-\cos \left (2 x \right )+4 c_{1} \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.581 (sec). Leaf size: 41

DSolve[D[y[x],x]+Sin[2 x]Csc[2 y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} \arccos (-\cos (2 x)-2 c_1) \\ y(x)\to \frac {1}{2} \arccos (-\cos (2 x)-2 c_1) \\ \end{align*}