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Manipal MET2010MathematicsDifferential Equations

If the solution of the differential equation d y d x = a x+3 2 y+f represents a circle, then the value of a is

Options

  1. A2
  2. B-2
  3. C3
  4. D-4

Correct answer

B. -2

Step-by-step solution

We have, d y d x = a x+3 2 y+f (a x+3) d x=(2 y+f) d y On integrating, we obtain a x^2 2 +3 x=y^2+f y+c - a 2 x^2+y^2-3 x+f y+c=0 This will represent a circle, if - a 2 =1 ( . coefficient of x^2= coefficient of .y^2 ) a=-2

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