Question

Substitution as suggested by the equation

sinxsinydx + cosxcosydy = 0

Answer 1

$\sin x \sin y dx+\cos x \cos y dy=0$

$\frac{\sin x }{\cos x} dx=-\frac{\cos y}{ \sin y} dy$

$-\frac{d\cos x }{\cos x}=-\frac{d\sin y}{ \sin y}$

$\ln|\cos x|=\ln|\sin y|+\ln C$

$\cos x=C\sin y$

Answer: $\cos x=C\sin y$.