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AP EAMCET202120 Aug 2021Morning ShiftMathematicsDifferential EquationsActual

The solution of the differential equation 2 x d y d x - y = 4 represents a family of

Options

  1. AEllipses
  2. BParabolas
  3. CStraight lines
  4. DCircles

Correct answer

B. Parabolas

Step-by-step solution

Given differential equation is 2 x d y d x - y = 4 . . ⇒ 2 x d y d x = 4 + y ⇒ 2 d y 4 + y = d x x On integrating both sides, we get ⇒ ∫ 2 4 + y d y = ∫ 1 x d x ⇒ 2 log 4 + y = log x + log c Using log a + log b = log a b and log a n = n log a , ⇒ log 4 + y 2 = log x c ⇒ y + 3 2 = c x , which is of the form y - k 2 = 4 a x - h and this is the general equation of a parabola. Thus, the equation y + 3 2 = c x , represents a family of parabolas.

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