Question Number 103089 by  M±th+et+s last updated on 12/Jul/20

solve:  (sin^2 (x)−y)dx−tan(x)dy=0

Answered by Ar Brandon last updated on 12/Jul/20

⇒{tanx(dy/dx)+y=sin^2 x}∙cosx  ⇒sinx(dy/dx)+ycosx=sin^2 xcosx  ⇒(d/dx)(ysinx)=sin^2 xcosx  ⇒ysinx=∫sin^2 xcosxdx=((sin^3 x)/3)+C  ⇒y=((sin^2 x)/3)+(C/(sinx))