If dy/dx = 2^(x+y) - 2^x/2^y, y(0) = 1, then y(1) is equal to :

Question

If 

\(\cfrac{dy}{dx}= \cfrac{2^{x+y}-2^x}{2^y}, \)

dy/dx = 2^x+y - 2^x/2^y, 

y(0) = 1, then y(1) is equal to : 

(1) log₂ (2 + e) 

(2) log₂ (1 + e) 

(3) log₂ (2e) 

(4) log₂ (1 + e² )

Answer 1

Correct answer is: (2) log₂ (1 + e)