Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Consider the family of all circles whose centers lie on the st

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 $P y^{p r i m e p r i m e} + Q y^{p r i m e} + 1 = 0,$ where $P, Q$ are functions of $x, y$ and $y^{p r i m e} (h e r e y^{p r i m e} = \frac{d y}{d x}, y^{=} \frac{d ^{2} y}{d x ^{2}}),$ then which of the following statements is (are) true? (a) $P = y + x$ (b) $P = y - x$ (c) $P + Q = 1 - x + y + y^{p r i m e} + (y^{p r i m e})^{2}$ (d) $P - Q = x + y - y^{p r i m e} - (y^{p r i m e})^{2}$

Views: 681 students

Found 5 tutors discussing this question

James Discussed

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

P y^{p r i m e p r i m e} + Q y^{p r i m e} + 1 = 0,

where

P, Q

are functions of

x, y

and

y^{p r i m e} (h e r e y^{p r i m e} = \frac{d y}{d x}, y^{=} \frac{d ^{2} y}{d x ^{2}}),

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

P = y + x

(b)

P = y - x

(c)

P + Q = 1 - x + y + y^{p r i m e} + (y^{p r i m e})^{2}

(d)

P - Q = x + y - y^{p r i m e} - (y^{p r i m e})^{2}

8 mins ago

Discuss this question LIVE

8 mins ago

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text

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

P y^{p r i m e p r i m e} + Q y^{p r i m e} + 1 = 0,

where

P, Q

are functions of

x, y

and

y^{p r i m e} (h e r e y^{p r i m e} = \frac{d y}{d x}, y^{=} \frac{d ^{2} y}{d x ^{2}}),

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

P = y + x

(b)

P = y - x

(c)

P + Q = 1 - x + y + y^{p r i m e} + (y^{p r i m e})^{2}

(d)

P - Q = x + y - y^{p r i m e} - (y^{p r i m e})^{2}

Filo tutor solution