1.

Form the differential equation representing the family of curves y = mx where m is arbitrary constant.

Answer»

The given family of curves represents the equation of straight lines. 

∴ y = mx ………. (1) 

Differentiate w.r.t x, we get dy

dy/dx = m

∴ substitute m = dy/dx, we have

y = mx

⇒ y = dy/dx x

dy/dx = y/x

dy/dx - y/x = 0

which is the required differential equation.



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