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AP EAMCET201824 Apr 2018Morning ShiftMathematicsDifferential EquationsActual

If a and b are arbitrary constants, then the differential equation having x^2 a^2 + y^2 b^2 =1 as its general solution is

Options

  1. A( d^2 y d x^2 )^2= [1+ ( d y d x )^2 ]^3
  2. B(x^2-y^2 ) d^2 y d x^2 -2 x y d y d x -y=0
  3. Cx y d^2 y d x^2 +x ( d y d x )^2-y d y d x =0
  4. Dx^2 d^2 y d x^2 +2 x d y d x -2 y=0

Correct answer

C. x y d^2 y d x^2 +x ( d y d x )^2-y d y d x =0

Step-by-step solution

x^2 a^2 + y^2 b^2 =1 On differentiating, 2 x a^2 + 2 y b^2 d y d x =0 y x d y d x = -b^2 a^2 Again differentiating w.r.t. x aligned & y x d^2 y d x^2 + d y d x [ x d y d x -y x^2 ]=0 & x y d^2 y d x^2 + d y d x [x d y d x -y ]=0 & x y d^2 y d x^2 +x ( d y d x )^2-y d y d x =0 . aligned

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