Question

The equation of the curve passing through (1, 1) which satisfies the differential equation  dy/dx = e^{x - y} + x²e^-y is

(A) e^y = e^x + x/2 + 1/2

(B) e^y = e^x + x/3 - 1/2

(C) e^y = e^x + x³/3 - 1/3

(D) e^y = e^x - x³/3 + 1/3

Answer 1

Answer is (C) e^y = e^x + x³/3 - 1/3

We have

Integrating, we get

The curve passes through (1, 1) implies

e = e + 1/3 + c

⇒ c = - 1/3

Therefore, the equation of the curve is

e^y = e^x + x³/3 - 1/3