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AP EAMCET2002MathematicsDifferential Equations

The solution of d y d x = ( x y )^ -1 / 3 is

Options

  1. Ax^ 2 / 3 +y^ 2 / 3 =c
  2. By^ 2 / 3 -x^ 2 / 3 =c
  3. Cx^ 1 / 3 +y^ 1 / 3 =c
  4. Dy^ 1 / 3 -x^ 1 / 3 =c

Correct answer

B. y^ 2 / 3 -x^ 2 / 3 =c

Step-by-step solution

We have, gathered d y d x = ( x y )^ -1 / 3 y^ -1 / 3 d y=x^ -1 / 3 d x gathered On integrating both sides, we get aligned & y^ -1 / 3+1 - 1 3 +1 = x^ -1 / 3+1 - 1 3 +1 +c^ & y^ 2 / 3 2 / 3 = x^ 2 / 3 2 / 3 +c^ & y^ 2 / 3 -x^ 2 / 3 = 2 3 c^ =c & aligned

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