The differential equation which represents the family of curves

• Differential Equation

The differential equation which represents the family of curves y = c₁e^c₂x where c₁ and c₂ are arbitrary constants, is

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

Answer

y = c₁e^c₂x

y' = c₁c₂e^c₂x

y' = c₂y

y'' = c₂y'

The correct option is D.