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

Explanation

`cosy*dy+cosxsinydx=0`
`implies (cosy)/(siny)dy+cosxdx=0`
Inetegrate both sides
`int(cosy)/(siny)dy+intcosxdx=0` Let `siny=t`
`impliesint(1)/(t)dt+intcosxdx=0`
`impliescosydy=dt`
`implieslogt+sinx=c`
`implies log(siny)+sinx=c`…..`(1)`
Given that `x=pi//2` if `y=pi//2`
`:. log sin"(pi)/(2)+sin"(pi)/(2)=c`
`impliesc=1`
`:.` From eq. `(1)`
`log(siny)+sinx=1`.