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The differential equation of the family of straight lines y = mx is

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TNUSRB SI 2010 Official Paper (Held on 04 July 2010)
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  2. ydx - xdy = 0
  4. y dx + x dy = 0

Answer (Detailed Solution Below)

Option 1 :
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Detailed Solution

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Explanation:

The differential equation of the family of straight lines y=mxy=mx can be obtained by differentiating both sides with respect to xx .
 
The derivative of yy with respect to xx is dy/dxdy/dx , and the derivative of mxmx with respect to xx is mm , because mm is a constant. So, we have:
 
dy/dx=mdy/dx=m
 
This is the differential equation representing the family of straight lines y=mxy=mx . Therefore, the correct answer is option 1) dy/dx=mdy/dx=m .

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