Question

If xy + x ∙ e–y + y ∙ ex = x2 and (dy/dx) = [(A + y + e–y – 2x)/(B + ex + x)] then A + B =___

(a) yex + xe–y

(b) yex – xe–y

(c) ye–x + xe–y

(d) yex + xey

Answer 1

The correct option (b) yex – xe–y

Explanation:

xy + xe–y + yex = x2

∴ differentiating wrt x gives,

x (dy/dx) + y + xe–y [(– dy)/(dx)] + e–y + yex + ex (dy/dx) = 2x

∴ (dy/dx) (x – xe–y + ex) = 2x – yex – e–y – y

∴ (dy/dx) = [(2x – y – e–y – yex)/(x – xe–y + ex)]

and given is (dy/dx) = – [(A + y + e–y – 2x)/(B + ex + x)]

∴ A = yex and B = – xe–y

∴ A + B = yex – xe–y