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MHT CET202121 Sep 2021Morning ShiftMathematicsDifferential EquationsActual

The differential equation of family of circles whose centre lie on X -axis is

Options

  1. Ad^2 y d x^2 + ( d y d x )^2+1=0
  2. By ( d^2 y d x^2 )+ ( d y d x )^2+1=0
  3. Cy ( d^2 y d x^2 )- ( d y d x )^2-1=0
  4. Dy ( d^2 y d x^2 )+ ( d y d x )^2-1=0

Correct answer

B. y ( d^2 y d x^2 )+ ( d y d x )^2+1=0

Step-by-step solution

Let (h, 0) be the centre of the circle and ' r ' be the radius. ( x - h )^2+( y -0)^2= r ^2 ( x - h )^2+ y ^2= r ^2 Differentiating w.r.t. x , we get 2( x - h )(1)+2 y dy dx =0 h = x + y dy dx Substituting value of ' h ' in eq. (1), we get y^2 ( d y d x )^2+y^2=r^2 y^2 [1+ ( d y d x )^2 ]=r^2 Differentiating w.r.t. x , we get aligned & y^2 (2 d y d x d^2 y d x^2 )+ [1+ ( d y d x )^2 ] 2 y d y d x =0 & y d^2 y d x^2 + ( d y d x )^2+1=0 aligned

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