Internal problem ID [4360]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 1.6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 47
dsolve(sec(x)^2*tan(y(x))+sec(y(x))^2*tan(x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\arctan \left (\frac {2 \tan \left (x \right ) c_{1}}{c_{1}^{2} \tan \left (x \right )^{2}+1}, \frac {c_{1}^{2} \tan \left (x \right )^{2}-1}{c_{1}^{2} \tan \left (x \right )^{2}+1}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.457 (sec). Leaf size: 68
DSolve[Sec[x]^2*Tan[y[x]]+Sec[y[x]]^2*Tan[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \arccos (-\tanh (\text {arctanh}(\cos (2 x))+2 c_1)) \\ y(x)\to \frac {1}{2} \arccos (-\tanh (\text {arctanh}(\cos (2 x))+2 c_1)) \\ y(x)\to 0 \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}