Internal problem ID [3141]
Book: An introduction to the solution and applications of differential equations, J.W. Searl,
1966
Section: Chapter 4, Ex. 4.2
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \left (x -1\right ) y^{\prime }-\cot \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 52.823 (sec). Leaf size: 59
DSolve[x*(x-1)*y'[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 ) y(x)\to -\frac {\pi }{2} y(x)\to \frac {\pi }{2} \end{align*}