Find the particular solution of the differential equation ex tan y dx + (2 - ex) sec²y dy = 0, given that y = π/4 when x = 0.

ex tan y dx = -(2 - ex) sec²y dy
-(2 - ex)⁻¹ dx = sec²y/tan y dy
Integrating both sides.
∫-(2 - ex)⁻¹ dx = ∫sec²y/tan y dy
=> log(tan y) = log(2 - ex) + c
c = log(tan y) - log(2 - ex) = log(tan y / (2 - ex))
Putting y = π/4, x = 0
c = log(1/1) => c = 0
=> log(tan y) = log(2 - ex)