29.4.26 problem 115

Internal problem ID [4717]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 115
Date solved : Monday, January 27, 2025 at 09:33:51 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.233 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 5.307 (sec). Leaf size: 47

DSolve[D[y[x],x]+Cot[x] Cot[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

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