Question

The elimination of the arbitrary constant m from the equation y = e^mx gives the differential equation ______.

Options

• `("d"y)/("d"x) = (y/x)log y`

• `("d"y)/("d"x) = (1/y)log y`

• `("d"y)/("d"x) = (x/y)log y`

• `("d"y)/("d"x) = (x/y)log x`

Answer 1

The elimination of the arbitrary constant m from the equation y = e^mx gives the differential equation `("d"y)/("d"x) = (y/x)log y`.

Explanation:

y = e^mx 

⇒ log y = mx    ......(i)

Differentiating w.r.t. x, we get

`1/y*("d"y)/("d"x)` = m

⇒ `1/y*("d"y)/("d"x) = logy/x`  .......[From (i)]

⇒ `("d"y)/("d"x) = (y/x)log y`