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JEE Main2012MathematicsDifferential EquationsActual

The integrating factor of the differential equation (x^2-1 d y d x +2 ) x y=x is

Options

  1. A1 x^2-1
  2. Bx^2-1
  3. Cx^2-1 x
  4. Dx x^2-1

Correct answer

B. x^2-1

Step-by-step solution

Given differential equation is aligned & (x^2-1 ) d y d x +2 x y=x & d y d x + 2 x x^2-1 y= x x^2-1 aligned This is in linear form. aligned & Integrating factor = 2 x x^2-1 d x= _e d t t & where aligned & =x^2-1 & =e^ t =x^2-1 aligned aligned Hence, required integrating factor =x^2-1 .

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