Find the solution of the differential equation `cos ydy+cosxsinydx=0` given that `y=pi//2` , when `x=pi//2.`

Explanation

Given,`cosydy+cosxsinydx=0`

⇒`cotydy=−cosxdx`

Now integrating, we get

`lnsiny=−sinx+C`

⇒`lnsiny+sinx=C`

Put` x=pi/2​ `and `y=pi/2`​, we get

`lnsin(pi/2)​+sin(pi/2)​=C
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