Q.435. Differential Equation.

Question 435.
sinx.cosx.dy/dx - y = sinx

Answer 435.
sinx cos x dy/dx - y = sin x
=> tanx dy/dx - y sec^2x = sec x tan x (dividing by cos^2 x)
=> (tanx dy/dx - y sec^2x) / tan^2 x = csc x (dividing by tan^2 x)
=> d/dx ( y / tan x ) = csc x
=> d ( y / tan x) = csc x dx

Integrating,
y / tan x = ∫ csc x dx - ln c
=> y / tan x = ln [ l tan (x/2) l / c ]
=> tan (x/2) / c = e^(y/tan x)
=> tan(x/2) = c*e^(y/tan x)

Link to YA!