Question

The general solution of the differential equation \[ \frac{dy}{dx}=e^{x-y}+x^2e^{-y} \] is

• A. \(e^{-y}=e^x+\frac{x^3}{3}+c\)
• B. \(e^y=e^x+\frac{x^3}{3}+c\)
• C. \(e^y=e^x+x^3+c\)
• D. \(e^y=e^x+c\)

Hint:

If \(e^{-y}\) appears in a differential equation, multiply by \(e^y\) to form \(\frac{d}{dx}(e^y)\).

Answer 1

The Correct Option is B