Question

If sin x is the integrating factor (IF) of the linear differential equation `dy/dx + Py` = Q then P is ______.

Options

• log sin x

• cos x

• tan x

• cot x

Answer 1

If sin x is the integrating factor (IF) of the linear differential equation `dy/dx + Py` = Q then P is cot x.

Explanation:

Since, IF of `dy/dx + Py` = Q is given by

IF = `e^(int pdx)`

So, sin x = `e^(int pdx)`

After differentiating on both sides, we get

cos x = `e^(int pdx)` cos x

= sin x P

`\implies` P = cot x