sinx dy/dx +3y =cosx

sinx. dy/dx+3y = cosx
dy/dx + 3/sinx.y = cosx/sinx
dy/dx + 3cosecx.y =cotx
I.F= e int. 3cosec.dx
=e ^log| cosecx - cotx|^3
= cosecx - cotx
y.(cosecx -cotx) = int. cotx(cosecx - cotx)
= int. cotx.cosecx- int. cot^2xdx
= - cosecx - int(cosec^2x-1)dx
= - (cosecx - cotx) + x +1
y = -1 + (x+c)/(cosecx - cotx