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AP EAMCET202423 May 2024Morning ShiftMathematicsDifferential EquationsActual

If y= ( ⁻¹ 2 x )^2+ ( ⁻¹ 2 x )^2 , then (1+4 x^2 )^2 y^ -16=

Options

  1. A8 x y^
  2. B-8 x (1+4 x^2 ) y^
  3. C8 x (1+4 x^2 ) y^
  4. D-8 x y^

Correct answer

B. -8 x (1+4 x^2 ) y^

Step-by-step solution

y= ( ⁻¹ 2 x )^2+ ( ⁻¹ 2 x )^2 aligned & d y d x = 4 ⁻¹ 2 x 1+4 x^2 - 4 ⁻¹ 2 x 1+4 x^2 & y^ = 4 ⁻¹ 2 x-4 ⁻¹ 2 x 1+4 x^2 & (1+4 x^2 ) y^ =4 ⁻¹ 2 x-4 ⁻¹ 2 x & 8 x y^ + (1+4 x^2 ) y^ = 8 (1+4 x^2 ) + 8 (1+4 x^2 ) & (1+4 x^2 )^2 y^ -16=-8 x (1+4 x^2 ) y^ aligned

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