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Solution of the differential equation x d y=y( x-y) d x, 0 < x < 2 is

Options

  1. Ay x= x+c
  2. By x= x+c
  3. Cx=( x+c) y
  4. Dx=( x+c) y

Correct answer

D. x=( x+c) y

Step-by-step solution

aligned & x d y=y( x-y) d x & d y d x =y x-y^2 x & 1 y^2 d y d x - 1 y x=- x & Let 1 y =t & - 1 y^2 d y d x = d t d x & - d y d x -t x=- x d t d x +( x) t= x . & I.F. =e^ f x d x = x aligned Solution is t ( . I.F) = (I.F) x d x 1 y x= x+c

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