UPSC NDA Math Model Paper 4

y=mx⇒

dy

dx

=m
∴y=

dy

dx

x⇒x

dy

dx

−y=0 is the required differential equation.
Note: The order of a differential equation representing a family of curves is same as the number of arbitrary constants present in the equation corresponding to the family of curves. In this equation i.e. y = mx there is one constant so order of differential equation is one.