If `sinx` is an integrating factor of the differential equation `(dy)/(dx)+P y=Q` , then write the value of `Pdot`

Options

A. log sin x
B. cos x
C. tan x
D. cot x

Answer

D

Explanation

We know that, If of `(dy)/(dx)+Py=Q` is
`IF=e^(int pdx)`
`sin x=e^(int p dx)`
On differentiating both sides, we get
`cosx=e^(int pdx)P`
`cos x=sin xP `
`Rightarrow P=cot x`