Differential Equation

The differential equation which represents the family of curves y = c1ec2x where c1 and c2 are arbitrary constants, is

  1. yy'' = y'
  2. y'' = y'y
  3. y' = y2
  4. yy'' = (y')2

Answer

y = c1ec2x

y' = c1c2ec2x

y' = c2y

y'' = c2y'

The correct option is D.