Question

The differential equation which represents the family of curves y = e^Cx is

A. y₁ = C₂ y

B. xy₁ – ln y = 0

C. x ln y = yy₁

D. y ln y = xy₁

Answer 1

Correct answer is D.

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