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The solution of e ^ y-x d y ~d x = y( x+ x) (1+y y) is

Options

  1. Ae ^y y = e ^x x+ c , where c is a constant of integration.
  2. Be ^y y= e ^x x+ c , where c is a constant of integration.
  3. Ce ^y y= e ^x x+ c , where c is a constant of integration.
  4. De ^y y= e ^x x+ c , where c is a constant of integration.

Correct answer

C. e ^y y= e ^x x+ c , where c is a constant of integration.

Step-by-step solution

array ll & e ^ y-x d y ~d x = y( x+ x) (1+y y) & e ^y (1+y y) y ~d y= e ^x( x+ x) d x & e ^y ( y+ 1 y ) d y= e ^x( x+ x) d x & e ^y y= e ^x x+ c & [ e ^x ( f (x)+ f ^ (x) ) d x= e ^x f (x)+ c ] array

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