PrepRung
Sign inSign up free

NDA 2016 Maths · Mathematics · Differential Equations · medium

The solution of dy/dx=e^x-y is

Single correct option

The solution of dydx=ex−y\dfrac{dy}{dx}=e^{x-y} is
  1. A. ey=ex+ce^y=e^x+c
  2. B. e−y=ex+ce^{-y}=e^{x}+c
  3. C. y=ex+cy=e^x+c
  4. D. ey=e−x+ce^{y}=e^{-x}+c
Show answer and solution

Answer: (A) ey=ex+ce^y=e^x+c

Write ey dy=ex dxe^y\,dy=e^x\,dx by separating variables. Integrating gives ey=ex+ce^y=e^x+c. Note ex−y=ex/eye^{x-y}=e^x/e^y, so eye^y must go to the left side; keeping e−ye^{-y} there is the usual error.
Report a mistake

Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake