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MHT CET202019 Oct 2020Morning ShiftMathematicsDifferential EquationsActual

The integrating factor of differential equation (1+y+x² y ) d x+ (x+x³ ) d y=0 is

Options

  1. A1 x
  2. Bx
  3. Cx
  4. De^ x

Correct answer

B. x

Step-by-step solution

(A) We have (1+y+x² y ) d x+ (x+x³ ) d y=0 d y d x = - (1+y+x² y ) x (1+x² ) = - [1+y (1+x² ) ] x (1+x² ) d y d x = -1 x (1+x² ) - y (1+x² ) x (1+x² ) d y d x + ( 1 x ) y= -1 x (1+x² ) I.F. =e^ 1 x d x =e^ x =x

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