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NDA2019MathematicsDifferential EquationsActual

The solution of the differential equation d y d x = ( y - x )+1 is

Options

  1. Ae ^ x [ ( y - x )- ( y - x )]= c
  2. Be ^ x [ ( y - x )+ ( y - x )]= c
  3. Ce ^ x ( y - x ) ( y - x )= c
  4. De^x=c (y-x) (y-x)

Correct answer

A. e ^ x [ ( y - x )- ( y - x )]= c

Step-by-step solution

d y d x = (y-x)+1 ...(1) Let y - x = t d y d x -1= d t d x (1) d t d x +1= t+1 aligned & d t d x = t & t dt =1 dx & t d t= 1 d x & | sect + t|= x + c & - | t- t|= x + c & | t- t|=- x - c & ( ( y - x )- ( y - x )=- x - c & ( y - x )- ( y - x )= e ^ - x e ^ - c & e ^ x ( ( y - x )- ( y - x ))= c aligned

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