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

y = c₁e^(c₂x) (i)
→y′ = c₁c₂e^(c₂x) →y′ = c₂y … (from (i)) (ii)
→y′′ = c₂y′ (iii)
From (ii) & (iii)
y′′ = c₂y′ = (y′/y)y′ = (y′)²/y
yy′′ = (y′)²
Hence, option 'C' is correct.