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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 the family of circles is represented by the differential equation `Py^('')+Qy^(')+1=0`, where P, Q are functions of x, y and `y^(')` (here `y^(')=(dy)/(dx),y^('')=(d^(2)y)/(dx^(2))`, then which of the following statements is (are) true?

A

`p=y+x`

B

`p=y-x`

C

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

D

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

Text Solution

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The correct Answer is:
B, C
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