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Consider the family of all circles whose...

Consider the family of all circles whose centers lie on the straight line `y=x` . If this family of circles is represented by the differential equation `P y''+Q y'+1=0,` where `P ,Q` are functions of `x , y` and `y^(prime)(here, y^(prime)=(dy)/(dx),y''=(d^2y)/(dx^2)),` then which of the following statements is (are) true?

A

A) `P=y+x`

B

B) `P=y-x`

C

C) `P+Q=1-x+y+y'+(y')^(2)`

D

D) `P-Q=x+y-y'-(y')^(2)`

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The correct Answer is:
B, C, D
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