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MHT CET202523 Apr 2025Evening ShiftMathematicsDifferential EquationsActual

The differential equation whose solution is A x^2+ By ^2=1 where A and B are arbitrary constants is of

Options

  1. Adegree 1 and order 2
  2. Bdegree 2 and order 1
  3. Cdegree 3 and order 2
  4. Ddegree 1 and order 3

Correct answer

A. degree 1 and order 2

Step-by-step solution

The differential equation is formed by eliminating the two arbitrary constants A and B from the equation A x^2 + B y^2 = 1 . Differentiating with respect to x gives 2 A x + 2 B y y' = 0 , simplifying to A x + B y y' = 0 . A second differentiation yields A + B ( (y')^2 + y y'' ) = 0 . To eliminate A and B , solve the first derivative equation for A as A = - B y y' x . Substitute into the second derivative equation: - B y y' x + B ( (y')^2 + y y'' ) = 0 . Divide throughout by B (which is nonzero for nontrivial soluti

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