Internal problem ID [2000]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 10, page 41
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\cos \left (y\right )^{2}+\left (x -\tan \left (y\right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve(cos(y(x))^2+(x-tan(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \arctan \left (\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-x -1}\right )+x +1\right ) \]
✓ Solution by Mathematica
Time used: 60.291 (sec). Leaf size: 21
DSolve[Cos[y[x]]^2+(x-Tan[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arctan \left (W\left (c_1 \left (-e^{-x-1}\right )\right )+x+1\right ) \]