Question

Find the particular solution of the differential equation (1 + e^2x)dy + (1 + y²)e^xdx = 0, given that y = 1, when x = 0.

Answer 1

Given differential equation is

(1 + e^2x)dy + (1 + y²)e^xdx = 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.