Exponential growth or decay form for JEE

Formula

\(\dfrac{dy}{dx}=ky\Rightarrow \dfrac{dy}{y}=k\,dx\Rightarrow y=Ce^{kx}\)

Variables: \(k\) is a constant, \(C\) is an arbitrary constant.

Conditions: Valid for \(y\neq 0\) during separation; \(y=0\) is also a solution.

Standard separable model; repeated in growth-decay type questions.