CUET and UG exam WB JEE Mock Test Series 2025 Mathematics Differential Calculus Second Order Derivatives
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 \(y'=\frac {dy}{dx}, y''=\frac {d^2y}{dx^2}\)), then which of the following statements is (are) true?
1
\(P=y+x\)
2
\(P=y-x\)
3
\(P+Q=1-x+y+y'+(y')^2\)
4
\(P-Q=x+y-y'-(y')^2\)