Given differential equation is

(1 + e^{2x})dy + (1 + y^{2})e^{x}dx = 0

Above equation may be written as

On integrating both sides, we get

On putting e^{x} = t or e^{x} dx = dt in RHS, we get

Also, given that y = 1, when x = 0.

On putting above values in Eq. (i), we get

On putting C = pi/2 in Eq. (i), we get

which is the required solution.