Internal problem ID [3851]
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: 0.11 (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: 6.097 (sec). Leaf size: 75
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 \arctan \left (e^{2 c_1} \cot (x)\right ) \\ y(x)\to 0 \\ y(x)\to \frac {1}{2} \pi \tan (x) \sqrt {\cot ^2(x)} \\ y(x)\to \frac {1}{2} \pi \left ((-1)^{\left \lfloor \frac {\arg (\cot (x))}{\pi }+\frac {1}{2}\right \rfloor }-\sqrt {\tan ^2(x)} \cot (x)\right ) \\ \end{align*}