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MHT CET202415 May 2024Morning ShiftMathematicsDifferential EquationsActual

The differential equation, having general solution as A x^2+ B y^2=1 , where A and B are arbitrary constants, is

Options

  1. Ax y ~d ^2 y ~d x^2 -x ( ~d y ~d x )^2-y ~d y ~d x =0
  2. Bx y ~d ^2 y ~d x^2 -x ( ~d y ~d x )^2+y ~d y ~d x =0
  3. Cx y ~d ^2 y ~d x^2 +x ( ~d y ~d x )^2+y ~d y ~d x =0
  4. Dx y ~d ^2 y ~d x^2 +x ( ~d y ~d x )^2-y ~d y ~d x =0

Correct answer

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

Step-by-step solution

A x^2+ B y^2=1 Differentiating w.r.t. x , we get 2 ~A x+2 ~B y ~d y ~d x =0...(i) Again, differentiating w.r.t. x , we get 2 ~A +2 ~B [ ( ~d y ~d x )^2+y ~d ^2 y ~d x^2 ]=0...(ii) Solving (i) and (ii), we get x y ~d ^2 y ~d x^2 +x ( ~d y ~d x )^2-y ~d y ~d x =0

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