Internal problem ID [2857]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 108.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (\sec ^{2}\relax (x )\right ) \cot \relax (y) \cos \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(diff(y(x),x) = sec(x)^2*cot(y(x))*cos(y(x)),y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {1}{\tan \relax (x )+c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 0.884 (sec). Leaf size: 45
DSolve[y'[x]==Sec[x]^2 Cot[y[x]] Cos[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}(\tan (x)+2 c_1) \\ y(x)\to \sec ^{-1}(\tan (x)+2 c_1) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}