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Manipal MET2018MathematicsDifferential Equations

The general solution of x (1+y^2 )^ 1 / 2 d x+y (1+x^2 )^ 1 / 2 d y=0 is

Options

  1. A⁻¹ x+ ⁻¹ y=c
  2. Bx^2+y^2= (1+x^2 )^ 1 / 2 + (1+y^2 )^ 1 / 2 +c
  3. C(1+x^2 )^ 1 / 2 + (1+y^2 )^ 1 / 2 =c
  4. D⁻¹ x- ⁻¹ y=c

Correct answer

C. (1+x^2 )^ 1 / 2 + (1+y^2 )^ 1 / 2 =c

Step-by-step solution

Given equation can be rewritten as x (1+x^2 )^ 1 / 2 d x+ y (1+y^2 )^ 1 / 2 d y=0 On integrating, we get 1+x^2 + 1+y^2 =c

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