Question

Form the differential equation corresponding to y = e^mx by eliminating m.

Answer 1

Given equation, y = e^mx

On differentiating the above equation with respect to x we get

\(\frac{dy}{dx}\) = me^mx

But y = e^mx

\(\therefore \frac{dy}{dx} =\) my

Now we have, y = e^mx

Applying log on both sides, we get,

log y = mx

which gives m = \(\frac{\text{log y}}{\text{x}}\)

So, putting this value of m in \(\frac{dy}{dx} = \) my we get

Hence, \(x\frac{dy}{dx} = \) y log y is the differential equation corresponding to y = e^mx.