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MHT CET202020 Oct 2020Evening ShiftMathematicsDifferential EquationsActual

The solution of the differential equation x ( y x ) d y= [y ( y x )-x ] d x is

Options

  1. A( x y )= |x|+c
  2. B( y x )= |y|+c
  3. C( y x )= |x|+c
  4. D( x y )= |y|+c

Correct answer

C. ( y x )= |x|+c

Step-by-step solution

We have x ( y x ) d y= [y ( y x )-x ] d x d y d x = y ( y x )-x x ( y x ) = ( y x )- 1 ( y x ) d y d x - ( 1 x ) y=- cosec ( y x ) Put y x =v y=v x d y d x =v+x d v d x ( v + xdv dx )- v =- cosec v x dv dx =- cosec v dv cosec v =- d x x v dv =- | x |- v=- |x|+c₁ x+c= v ( y x )= |x|+c

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