Question

The differential equation corresponding to the family of curves \[ y=\log_e(ax+3), \] where \(a\) is an arbitrary constant, is

• A. \(x\dfrac{dy}{dx}+3e^{-x}=1\)
• B. \(x\dfrac{dy}{dx}+3e^{y}=1\)
• C. \(x\dfrac{dy}{dx}+3e^{-y}=1\)
• D. \(x\dfrac{dy}{dx}+3e^{x}=1\)

Hint:

To form a differential equation from a family of curves: \[ \boxed{ \text{Differentiate the given equation and eliminate the arbitrary constant.} } \]

Answer 1

The Correct Option is C