The differential equation of the family
`y = ae^(x) + bx e^(x) + cx^(2)e^(x)` of curves where, a,b,c are arbitrary constants is

Options

A. `logy = tan x (dy)/(dx)`
B. ` y log y = tan x(dy)/(dx)`
C. ` y log y = sin x(dy)/(dx)`
D. ` log y = cos x (dy)/(dx)`

Answer

b

Explanation

Curve is ` y = e^(asinx) rArr sin x (logy)/a`
` :. (dy)/(dx) = e^(asinx) *a cos x `
` (dy)/(dx) = y cos x* (logy)/(sinx) " " [ :' a = (log y)/(siny)]`
` rArr y log y = tan x (dy)/(dx)`