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BITSAT2012MathematicsDifferential EquationsActual

The differential equation whose solution is A x²+B y²=1 where A and B are arbitrary constants is of

Options

  1. Asecond order and second degree
  2. Bfirst order and second degree
  3. Cfirst order and first degree
  4. Dsecond order and first degree

Correct answer

D. second order and first degree

Step-by-step solution

A x²+B y²=1 ...(1) A x+B y d y d x =0 ...(2) A+B y d² y d x² +B ( d y d x )²=0 ...(3) x -B y d² y d x² -B ( d y d x )² +B y d y d x =0 Dividing both sides by - B , we get x y d² y d x² +x ( d y d x )²-y d y d x =0 Which is a DE of order 2 and degree 1

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