(sin^2y+xcoty)y'=1的通解是?

(sin^2y+xcoty)y'=1的通解是?
(sin^2y+xcoty)y'=1的通解是?

(sin^2y+xcoty)y'=1的通解是?
我也给一种解法：
(sin^2y + xcoty)y'＝1
===> sin^2y dy + x coty dy ＝dx
===> sin^2y dy ＝ dx － x cosy/siny dy
===> siny dy ＝ (1/siny) dx + (－xcosy/sin^2y) dy
===> siny dy ＝d (x/siny)
===> ∫ siny dy ＝ ∫ d (x/siny)
===> －cosy ＝ x/siny + C
===> x/siny + cosy ＝ C (C为任意常数)
由于原题中有coty,所以还是不通分为好,以免影响定义域.

sin^2y是什么