Question

The family of curves y = `e^("a" sin x)`, where a is an arbitrary constant, is represented by the differential equation.

Options

• log y = tan x `"dy"/"dx"`

• y log y = tan x `"dy"/"dx"`

• y log y = sin x `"dy"/"dx"`

• log y = cos x `"dy"/"dx"`

Answer 1

y log y = tan x `"dy"/"dx"`

Explanation:

y = `e^("a" sin x)`

⇒ log y = a sin x   ...(i)

Differentiating w.r.t. x, we get

`1/y*"dy"/"dx"` = a cos x

⇒ a = `1/(y cos x)*"dy"/"dx"`

Putting the value of a in (i), we get

y log y = tan x `"dy"/"dx"`