Internal problem ID [3378]
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')`]
\[ \boxed {y^{\prime }-\tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x) = tan(x)*(tan(y(x))+sec(x)*sec(y(x))),y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (-\ln \left (\cos \left (x \right )\right ) \sec \left (x \right )+c_{1} \sec \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 9.719 (sec). Leaf size: 20
DSolve[y'[x]==Tan[x] (Tan[y[x]]+ Sec[x] Sec[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arcsin \left (\frac {1}{4} \sec (x) (-4 \log (\cos (x))+c_1)\right ) \]