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COMEDK2024MathematicsDifferential Equations

The solution of differential equation d y d x - ^2 y 1-x^2 =0

Options

  1. Ay= ⁻¹ x+C
  2. By= ⁻¹ x+C
  3. Cy= ⁻¹ x+C
  4. DNone of these

Correct answer

C. y= ⁻¹ x+C

Step-by-step solution

We have, d y d x = ^2 y 1-x^2 gathered d y ^2 y = d x 1-x^2 ^2 y d y= 1 1-x^2 d x gathered Integrate both sides, gathered ^2 y d y= 1 1-x^2 d x y= ⁻¹ x+C [ d x 1-x^2 = ⁻¹ x+C ] gathered

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