Internal problem ID [2869]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 120.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\tan \relax (x ) \left (\tan \relax (y)+\sec \relax (x ) \sec \relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 17
dsolve(diff(y(x),x) = tan(x)*(tan(y(x))+sec(x)*sec(y(x))),y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (-\ln \left (\cos \relax (x )\right ) \sec \relax (x )+c_{1} \sec \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 2.969 (sec). Leaf size: 20
DSolve[y'[x]==Tan[x] (Tan[y[x]]+ Sec[x] Sec[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcSin}\left (\frac {1}{4} \sec (x) (-4 \log (\cos (x))+c_1)\right ) \\ \end{align*}