Internal problem ID [2866]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 117.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\tan \relax (x ) \cot \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 11
dsolve(diff(y(x),x) = tan(x)*cot(y(x)),y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {\cos \relax (x )}{c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 5.251 (sec). Leaf size: 47
DSolve[y'[x]==Tan[x] Cot[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcCos}\left (\frac {1}{2} c_1 \cos (x)\right ) \\ y(x)\to \text {ArcCos}\left (\frac {1}{2} c_1 \cos (x)\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}