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Consider the family of all circles whose centers lie on
P the straight line \( y=x \). If this family of circles is repre-

WV sented by the differential equation Py" + Qy' + \( 1=0 \), where \( P, Q \) are functions of \( x, y \) and \( y^{\prime} \) (here
\( y^{\prime}=\frac{d y}{d x}, y^{\prime \prime}=\frac{d^{2} y}{d x^{2}} \) ), then which of the following [JEtatements is (are) true? Advanced-2015]
(a) \( \mathrm{P}=\mathrm{y}+\mathrm{x} \)
(b) \( P=y-x \)
(c) \( P+Q=1-x+y+y^{\prime}+\left(y^{\prime}\right)^{2} \)
(d) \( \mathrm{P}-\mathrm{Q}=\mathrm{x}+\mathrm{y}-\mathrm{y}^{\prime}-\left(\mathrm{y}^{\prime}\right)^{2} \)
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