Internal problem ID [2862]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 113.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+\tan \relax (x ) \sec \relax (x ) \left (\cos ^{2}\relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 18
dsolve(diff(y(x),x)+tan(x)*sec(x)*cos(y(x))^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = -\arctan \left (\frac {\cos \relax (x ) c_{1}+1}{\cos \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 1.734 (sec). Leaf size: 31
DSolve[y'[x]+Tan[x] Sec[x] Cos[y[x]]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcTan}(-\sec (x)+c_1) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}