Internal problem ID [2632]
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]
Solve \begin {gather*} \boxed {x \left (x -1\right ) y^{\prime }-\cot \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(x*(x-1)*diff(y(x),x)=cot(y(x)),y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {x}{c_{1} \left (x -1\right )}\right ) \]
✓ Solution by Mathematica
Time used: 49.463 (sec). Leaf size: 55
DSolve[x*(x-1)*y'[x]==Cot[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}\left (-\frac {e^{c_1} (x-1)}{x}\right ) \\ y(x)\to \sec ^{-1}\left (-\frac {e^{c_1} (x-1)}{x}\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}