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MHT CET20226 Aug 2022Evening ShiftMathematicsDifferential EquationsActual

The differential equation d y d x = 1-y^2 y determines a family of circles with

Options

  1. Avariable radii and a fixed centre at (0,-1)
  2. Bfixed radius of 1 unit and variable centres along the X -axis
  3. Cfixed radius of 1 unit and variable centres along the Y-axis
  4. Dvariable radii and a fixed centre at (0,1)

Correct answer

B. fixed radius of 1 unit and variable centres along the X -axis

Step-by-step solution

aligned & d y d x = 1-y^2 y & y d y 1-y^2 = d x & - 1-y^2 =x+c & 1-y^2=(x+c)^2 & (x+c)^2+y^2=1 aligned The above equation represents a circle having centre at (-c, 0) which is variable and radius is equal to ' 1 ' which is fixed.

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