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 Py ” + Qy ’ + 1 = 0, where P, Q are functions of x, y and y ’ (here y ’ = 
, y ” = 
), then which of the following statements is (are) true ?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(b,c)Let the family of circles be x 2 + y 2 – 
x – 
y + c = 0
On differentiation 2x + 2yy ’ – 
– 
y ’ = 0
Again on differentiation and substituting ‘ 
’ we get 
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