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The curve satisfying the differential equation d x d y = x + 2 y x 2 y - 2 x 3 and passing through ( 1 ,   0 ) is given by

Options

  1. Ax 2 + y 2 = 1
  2. Bx 2 + y 2 + y x = 1
  3. Cy 2 - y x - x 2 = - 1
  4. Dx 2 - y 2 = 1

Correct answer

B. x 2 + y 2 + y x = 1

Step-by-step solution

Given equation is 2 x d x + 2 y d y + d y x = 0 Integrating, we get, x 2 + y 2 + y x = c As ( 1 ,   0 ) lies on it, hence, c = 1

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