Solution of the differential equation (dy/dx) tan y= sin (x+y)+ sin (x-y) is:

Question

Solution of the differential equation (dy/dx) tan y= sin (x+y)+ sin (x-y) is: (A)  sec text y+2 text cos text x=c  (B)  sec text y-2 text cos text x=c  (C)  cos text y-2 text sin text x=c  (D)  tan text y-2 text sec text y=c

Tardigrade Admin · Accepted Answer

∵ (dy/dx) tan y= sin (x+y)+ sin (x-y) ⇒ (dy/dx) tan y=2 sin x cos y ⇒ ∫ tan y sec y dy=2∫ sin x dx ⇒ sec y+2 cos x=c

Q. Solution of the differential equation $\frac{d y}{d x} tan y = sin (x + y) + sin (x - y)$ is:

$sec y + 2 cos x = c$

$sec y - 2 cos x = c$

$cos y - 2 s in x = c$

$t an y - 2 sec y = c$

$sec y + 2 s in x = c$

$∵$ $\frac{d y}{d x} tan y = sin (x + y) + sin (x - y)$
$\Rightarrow$ $\frac{d y}{d x} tan y = 2 sin x cos y$
$\Rightarrow$ $\int tan y sec y d y = 2 \int sin x d x$
$\Rightarrow$ $sec y + 2 cos x = c$

Q. Solution of the differential equation dxdy​tany=sin(x+y)+sin(x−y) is:

secy+2cosx=c

secy−2cosx=c

cosy−2sinx=c

tany−2secy=c

secy+2sinx=c

∵ dxdy​tany=sin(x+y)+sin(x−y) ⇒ dxdy​tany=2sinxcosy ⇒ ∫tanysecydy=2∫sinxdx ⇒ secy+2cosx=c