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AP EAMCET2001MathematicsDifferential Equations

The solution of x^2+y^2 d y d x =4 is

Options

  1. Ax^2-1=C (1+y^2 )
  2. Bx^2+1=C (1-y^2 )
  3. Cx^2-1=C (1-y^2 )
  4. Dx^2+1=C (1-y^2 )

Correct answer

D. x^2+1=C (1-y^2 )

Step-by-step solution

We have, aligned x^2+y^2 d y d x & =4 y^2 d y & = (4-x^2 ) d x aligned On integrating both sides, we get array rlrl y^3 3 & =4 x- x^3 3 +C^ & y^3 & =12 x-x^3+C x^3+y^3 & =12 x+C array

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