The general solution of the differential equation (dy/dx) + sin (x + y) = sin (x -y) is

Question

The general solution of the differential equation (dy/dx) + sin (x + y) = sin (x -y) is (A)  log tan y + sin x = C (B)  log tan (y/2) + 2 sin x = C  (C)  tan (y/2) + log sin x = C  (D) None of these

Tardigrade Admin · Accepted Answer

The equation is, (d y/d x)= sin (x-y)- sin (x +y)=2 cos x sin (-y) ⇒ (d y/ sin y)+2 cos x d x=0 ⇒ ∫ textcosec y d y+2 ∫ cos x d x=C ⇒ log tan (y/2)+2 sin x=C

Q. The general solution of the differential equation $\frac{d y}{d x} + sin (x + y) = sin (x - y)$ is

$lo g tan y + sin x = C$

$lo g tan \frac{y}{2} + 2 sin x = C$

$tan \frac{y}{2} + lo g sin x = C$

None of these

The equation is,
$\frac{d y}{d x} = sin (x - y) - sin (x + y) = 2 cos x sin (- y)$
$\Rightarrow \frac{d y}{s i n y} + 2 cos x d x = 0$
$\Rightarrow \int cosec y d y + 2 \int cos x d x = C$
$\Rightarrow lo g tan \frac{y}{2} + 2 sin x = C$

Q. The general solution of the differential equation dxdy​+sin(x+y)=sin(x−y) is

logtany+sinx=C

logtan2y​+2sinx=C

tan2y​+logsinx=C