Question

The differential equation corresponding to primitive $y = e ^ { c x }$is

Or

The elimination of the arbitrary constant m from the equation $y = e ^ { m x }$ gives the differential equation

• A. $\frac { d y } { d x } = \left( \frac { y } { x } \right) \log x$
• B. $\frac { d y } { d x } = \left( \frac { x } { y } \right) \log y$
• C. $\frac { d y } { d x } = \left( \frac { y } { x } \right) \log y$
• D. $\frac { d y } { d x } = \left( \frac { x } { y } \right) \log x$

Answer 1

Answer: (C)

$\frac { d y } { d x } = \left( \frac { y } { x } \right) \log y$

Answer 2

$y = e ^ { m x }$ ⇒ $\log y = m x \Rightarrow m = \frac { \log y } { x }$

Now $y = e ^ { m x }$ ⇒ $\frac { d y } { d x } = m e ^ { m x } = \frac { \log y } { x } \cdot y = \left( \frac { y } { x } \right) \log y$