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Find the particular solution of the differential equation (1 + e2x)dy + (1 + y2)exdx = 0, given that y = 1, when x = 0.

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Given differential equation is

(1 + e2x)dy + (1 + y2)exdx = 0

Above equation may be written as

On integrating both sides, we get

On putting ex = t or ex 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.

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