I'm not very good at forming differential equations by word problems so I need some help with this question:

A curve passing through the point (1,1) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of P from the x-axis. Determine the equation of the curve.

  • $\begingroup$ Give it a shot. What formula do you come up with? $\endgroup$
    – The Count
    Apr 22, 2017 at 12:07
  • $\begingroup$ Think about orthagonal trajectories. $\endgroup$ Apr 22, 2017 at 12:37
  • $\begingroup$ I get 1= -(1/f'(1))+c given that the normal has the slope -1/f(x) at any point x. Then I substitute for c in the equation y=-1/f(x)+c . Post this, I find the distance from the orgin, and end up with (f'(x)^2)=(1+(f'(x))^2)/(1+(1/f'(1))^2 $\endgroup$
    – Reya
    Apr 22, 2017 at 13:27


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