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KCET2017MathematicsApplication of Derivatives

The integrating factor of the differential equation ( x d y d x +2 y=x² ) is ( (x 0) )

Options

  1. A( x² )
  2. Blog ( x )
  3. C( e^ x )
  4. D( x )

Correct answer

A. ( x² )

Step-by-step solution

Given differential equation [ array l x d y d x +2 y=x² d y d x + 2 x y=x array ] The general differential equation of this type is given by [ d y d x +P(x) y=Q(x) ] So, I.F. factor is given by ( I F =e^ P d x ) [ array l =e^ 2 x d x =e^ 2 x =e^ x² =x² array ]

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