27.2.2 problem 2

Internal problem ID [4302]
Book : An introduction to the solution and applications of differential equations, J.W. Searl, 1966
Section : Chapter 4, Ex. 4.2
Problem number : 2
Date solved : Monday, January 27, 2025 at 09:00:40 AM
CAS classification : [_separable]

\begin{align*} x \left (x -1\right ) y^{\prime }&=\cot \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 15

dsolve(x*(x-1)*diff(y(x),x)=cot(y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 60.119 (sec). Leaf size: 41

DSolve[x*(x-1)*D[y[x],x]==Cot[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\arccos \left (-\frac {e^{-c_1} x}{x-1}\right ) \\ y(x)\to \arccos \left (-\frac {e^{-c_1} x}{x-1}\right ) \\ \end{align*}