Differential EquationHard
Question
The differential equation of all circles in a plane must be 
Options
A.y3(1 + y12) - 3y1y22 = 0
B.of order 3 and degree 1
C.of order 3 and degree 2
D.y32(1 - y12) - 3y1y22 = 0
Solution
x2 + y2 + 2gx + 2fy + c = 0 (There are three arbitrary constants g, f and c)
2x + 2y .
+ 2g + 2f. 
= 0 ....... (1)
2 + 2y12 + 2yy2 + 2fy2 = 0 ........ (2)
4y1y2 + 2y1y2 + 2yy3 + 2f y3 = 0 ........ (3)
from (1) , (2) and (3)
y3(1 + y12) - 3y1y22 = 0
2x + 2y .
+ 2g + 2f. = 0 ....... (1)2 + 2y12 + 2yy2 + 2fy2 = 0 ........ (2)
4y1y2 + 2y1y2 + 2yy3 + 2f y3 = 0 ........ (3)
from (1) , (2) and (3)
y3(1 + y12) - 3y1y22 = 0
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