Question

Cos x cos y dx - sin x sin y dy=0

Answer 1

$cosx\cdot cosy\cdot dx-sinx\cdot siny\cdot dy=0\; |:(cosy\cdot sinx)\ne 0\\\\\int \frac{cosx\cdot dx}{sinx} =\int \frac{siny\cdot dy}{cosy} \\\\\int \frac{d(sinx)}{cosx} =\int \frac{-d(cosy)}{siny} \\\\ln|cosx|=-ln|siny|+ln|C|\\\\ln|cosx|+ln|siny|=ln|C|\\\\cosx\cdot siny=C\\\\siny=\frac{C}{cosx}\\\\y=arcsin(\frac{C}{cosx})$