Q.Find the differential equation of all the circles that pass through origin.
A.
Well, I have a plan but you'll need to put in the details.
If the circle passes through the origin then .
Then the equation of the circle becomes
.... (1)
Differentiate (1) with respect to x:
.... (2)
Differentiate (2) with respect to x:
.... (3)
Clearly k needs to be eliminated from (3).
(1) and (2) can be solved simultaneously to get k and h in terms of x, y and y'. You want k. Substitute the result into (3).