Q. 23

# Mark the correct alternative in each of the following:

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

A. y_{1} = C_{2} y

B. xy_{1} – ln y = 0

C. x ln y = yy_{1}

D. y ln y = xy_{1}

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 = xy_{1} = (D)

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