The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is

Question

The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is (A) (sin x/sin y)=c (B) sin x sin y = c (C) sin x + sin y =c (D) cos x cos y =c

Tardigrade Admin · Accepted Answer

cosx siny dx + sinx cosy dy = 0 (cos xdx/sin x)=-(cos ydx/sin y) On integrating, we get log sinx = - log siny + logc ⇒ log sinx+log siny=logc ⇒ sinx siny=c

Q. The solution of the differential equation $cos x s in y d x + s in x cos y d y = 0$ is

$\frac{s in x}{s in y} = c$

$s in x s in y = c$

$s in x + s in y = c$

$cos x cos y = c$

$cos x s in y d x + s in x cosy d y = 0$
$\frac{cos x d x}{s in x} = - \frac{cos y d x}{s in y}$
On integrating, we get
$l o g s in x = - l o g s in y + l o g c$
$\Rightarrow l o g s in x + l o g s in y = l o g c$
$\Rightarrow s in x s in y = c$

Q. The solution of the differential equation cosxsinydx+sinxcosydy=0 is

sinysinx​=c

sinxsiny=c

sinx+siny=c

cosxcosy=c