Question

Solve the differential equation (1 + cos2x)dy/dx - (1 + e^y)sin2x = 0; given that y = 0, when x = π/4.

Answer 1

(1 + cos2x)dy = (1 + e^y)sin2xdx

Separating the variables

Taking y = 0, when x = π/4 we get

0 + log(1/2√2) = A ⇒ A = - 3/2log2

The solution (called particular solution) is