Solve $\sec^2 x \cdot an y \, dx + \sec^2 y \cdot an x \, dy = 0$:

Question

Solve $\sec^2 x \cdot 	an y \, dx + \sec^2 y \cdot 	an x \, dy = 0$:

Accepted Answer

A. $	an x \cdot 	an y = c$

Rewrite: $(\sec^2 y/	an y)dy + (\sec^2 x/	an x)dx = 0$. Recognise each as a $du/u$: integrating gives $\log	an y + \log	an x = \log c$ ⇒ $	an x \cdot 	an y = c$.

Answer

$	an x + 	an y = c$

Answer

$\sec x + \sec y = c$

Answer

$\sin x \cdot \sin y = c$

Solve $\sec^2 x \cdot \tan y \, dx + \sec^2 y \cdot \tan x \, dy = 0$: