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Differential Equations question

2015 · Shift 1 · Q29

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JEE Advanced
Mathematics
Differential Equations
2015 · Shift 1 · Q29

Differential Equations question

2015 · Shift 1 · Q29

JEE AdvancedMathematicsDifferential EquationsMultiple correct+4 / −2

Consider the family of all circles whose centres lie on the straight line

y=x,

If this family of circle is represented by the differential equation

Py'' + Qy' + 1 = 0,

where

P, Q

are functions of

x,y

and

y'

\left( {here\,\,\,y' = {{dy} \over {dx}},y'' = {{{d^2}y} \over {d{x^2}}}} \right)

then which of the following statements is (are) true?

A
$P = y + x$
B
$\,P = y - x$
C
$\,P + Q = 1 - x + y + y' + {\left( {y'} \right)^2}$
D
$\,P - Q = 1 - x + y - y' - {\left( {y'} \right)^2}$

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