Question

The solution of $xco{s}^{2}ydx=yco{s}^{2}xdy$ is:

• A. $\tan x\tan y=c$
  
• B. $y\tan y=x\tan x+c$
• C. $\tan x\cos y=\tan y\cos x+c$
• D. $y\tan y-x\tan x+log\left(\frac{cosy}{cosx}\right)=c$

Answer 1

The correct option is D $y\tan y-x\tan x+log\left(\frac{cosy}{cosx}\right)=c$

$\Rightarrow \int xse{c}^{2}xdx=\int yse{c}^{2}ydy+c$
$\Rightarrow xtanx-\int tanxdx=ytany-\int tany+c$
$\Rightarrow xtanx-logsecx=ytany-logsecy+c$
$\Rightarrow ytany-xtanx+log\frac{cosy}{cosx}=c$