Internal problem ID [3372]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 114.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\cot \left (x \right ) \cot \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 13
dsolve(diff(y(x),x) = cot(x)*cot(y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \arccos \left (\frac {1}{\sin \left (x \right ) c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 5.785 (sec). Leaf size: 47
DSolve[y'[x]==Cot[x] Cot[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\arccos \left (-\frac {1}{2} c_1 \csc (x)\right ) y(x)\to \arccos \left (-\frac {1}{2} c_1 \csc (x)\right ) y(x)\to -\frac {\pi }{2} y(x)\to \frac {\pi }{2} \end{align*}