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MHT CET2009MathematicsDifferential Equations

Form the differential equation of all family of lines y=m x+ 4 m by eliminating the arbitrary constant ' m^ ' is

Options

  1. Ad² y d x² =0
  2. Bx ( d y d x )²-y d y d x +4=0
  3. Cx ( d y d x )²+y d y d x +4=0
  4. Dd y d x =0

Correct answer

B. x ( d y d x )²-y d y d x +4=0

Step-by-step solution

y=m x+ 4 m d y d x =m From Eq. (i), we get aligned y &=x ( d y d x )+ 4 (d y / d x) & y ( d y d x )=x ( d y d x )²+4 & x ( d y d x )²-y d y d x +4=0 aligned Which is the required differential equation.

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