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 ar functions of dy a, yandy (here y = dy y" = da dr? then which of the following statements is (are) true? (1) P = y + x (2) P = y -x (3) P+Q = 1- r +y +y + (y)

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 ar functions of dy a, yandy (here y = dy y" = da dr? then which of the following statements is (are) true? (1) P = y + x (2) P = y -x (3) P+Q = 1- r +y +y + (y)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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
dy
x, yandy' (here y
dx
dx2
then which of the following statements is (are) true?
(1) P = y + x
(2) P = y - x
(3) P+Q =1- x +y + y +
(4) P - Q = x +y-y

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