29.5.2 problem 117

Internal problem ID [4719]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 117
Date solved : Monday, January 27, 2025 at 09:33:57 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\tan \left (x \right ) \cot \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.255 (sec). Leaf size: 11

dsolve(diff(y(x),x) = tan(x)*cot(y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 5.322 (sec). Leaf size: 47

DSolve[D[y[x],x]==Tan[x] Cot[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

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