Ok, but I think it should be the other way round because the question was x cos[y] dx+ sin x dy=0 :
DSolve[y'[x] == (x Cos[y[x]])/Sin[x], y[x], x]
Thank you, Sir.
$Version (* "12.3.0 for Microsoft Windows (64-bit) (May 10, 2021)" *) DSolve[y'[x] == Sin[x]/(x Cos[y[x]]), y[x], x] (*{{y[x] -> ArcSin[C[1] + SinIntegral[x]]}}*)
