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MHT CET202122 Sep 2021Morning ShiftMathematicsDifferential EquationsActual

The differential equation of all family of lines y=m x+ 4 m obtained by eliminating the arbitrary constant m is

Options

  1. Ay ( d y d x )=4
  2. By ( d y d x )^2+y ( d y d x )+4=0
  3. Cx ( d y d x )+4=0
  4. Dx ( d y d x )^2-y ( d y d x )+4=0

Correct answer

D. x ( d y d x )^2-y ( d y d x )+4=0

Step-by-step solution

aligned & y=m x+ 4 m & d y d x =m aligned Substituting value of m in equation (1), we get aligned & y= ( d y d x ) x+ 4 ( d y d x ) & y ( d y d x )= ( d y d x )^2 x+4 aligned

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