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

Options

A. ` y sin x= C + soin 2x`
B. ` y cos x = C +1/2 sin 2x`
C. ` y cos x = C - sin 2x`
D. ` y cos x = C +1/2 cos 2x`

Answer

d

Explanation

Given , `(dy)/(dx) - y tan x = -2 sin x`
` :. IF = e^( - int tanx dx) cos x `
` :.` Solution is
` y (cos x ) = int -2 sin 2x dx +C`
` rArr y cos x = (cos 2x)/2 + C`