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NDA2019MathematicsDifferential EquationsActual

The differential equation which represents the family of curves given by y=c (1-e^x ) is

Options

  1. Ae^x y d x+ (1-e^x ) d y=0
  2. Be^x y d x+ (1-e^x ) ^2 y d y=0
  3. Ce^x (1-e^x ) d x+ y d y=0
  4. De^x y d y+ (1-e^x ) d x=0

Correct answer

B. e^x y d x+ (1-e^x ) ^2 y d y=0

Step-by-step solution

aligned & y=c (1-e^x ) & ^2 y d y d x =c (-e^x ) & c= 1 e^x ^2 y d y d x & y= -1 e^x ^2 y d y d x (1-e^x ) & e^x y= ^2 y (1-e^x ) d y d x & e^x y d x+ (1-e^x ) ^2 y d y=0 aligned

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