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AP EAMCET2003MathematicsDifferential Equations

Solution of d y d x = x x^2+x y+y y is

Options

  1. Ay y=x^2 x+C
  2. By y=x^2+C
  3. Cy y=x^2+ x
  4. Dy y=x x+C

Correct answer

A. y y=x^2 x+C

Step-by-step solution

We have, d y d x = x x^2+x y+y y ( y+y y) d y= (x x^2+x ) d x On integrating both sides, we get - y+y y+ y= x^2 2 x^2- x^2 2 + x^2 2 +C y y= x^2 2 x^2+C y y=x^2 x+C

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