Mark the correct alternative in each of the following: The differential equation which represents the family of curves y = e Cx is

Question

Philoid · Accepted Answer

y = e^Cx

Taking log both sides we get,

⇒ log y = log e^Cx

⇒ log y = Cx log e ∵ log a^x = x log a

⇒ log y = Cx --(1) ∵ log e = 1

Differentiate w.r.t x we get,

Put value of C in (1) we get,

Which is ⇒ y ln y = xy₁ = (D)