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The solution of the differential equation y 2 x 4 + y d y + 4 x y 2 - 1 x 2 d x = 0 is (where C is an arbitrary constant)

Options

  1. A3 x 2 y + x 3 - y 3 = C
  2. B3 x 4 y 2 + y 3 - x 3 = C
  3. C3 x 2 y 4 + x 3 - y 3 = C
  4. D3 x 2 y 4 + y 3 - x 3 = C

Correct answer

B. 3 x 4 y 2 + y 3 - x 3 = C

Step-by-step solution

2 x 4 y d y + y 2 d y + 4 x 3 y 2 d x - x 2 d x = 0 2 x 3 y x d y + 2 y d x + y 2 d y - x 2 d x = 0 2 x 2 y x 2 d y + 2 x y d x + y 2 d y - x 2 d x = 0 2 x 2 y d x 2 y + y 2 d y - x 2 d x = 0 On integrating, we get, x 2 y 2 + y 3 3 - x 3 3 = C 1 3 x 4 y 2 + y 3 - x 3 = C

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