Q84 / 150 · MHT CET 2016 · Mathematics

If sin⁡x is the integration factor of the linear differential equation dydx+Py=Q, then P is

  • A
    log⁡sin⁡x
  • B
    cos⁡x
  • C
    tan⁡x
  • Correct answer
    D
    cot⁡x

Solution

Given.
I.F of dydx+py=Q issin⁡ x
∴  e∫p dx=sin⁡x
⇒  ∫P dx=ln⁡sin⁡x
By anti - differentiation method, we will get
P=ddxln⁡sin⁡x
=1sin⁡x.cos⁡x
P=cot⁡x

Hence, the correct answer is option: 'D'.

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