Obtain the differential equations associated with the following general sets of curves. If there are n constants you will need an nth order differential equation. You will first need to find the general equation of the set of curves. Some of these need quite a lot of manipulation. (a) The set of circles centred at the point (-2,3). More generally, given a fixed point (a, b), what is the equation of the first order ODE representing the set of circles centred at that point?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
Question
(4) Obtain the differential equations associated with the following general sets of curves.
If there are n constants you will need an nth order differential equation. You will
first need to find the general equation of the set of curves. Some of these need quite
a lot of manipulation.
(a)
The set of circles centred at the point (-2,3). More generally, given
a fixed point (a, b), what is the equation of the first order ODE representing
the set of circles centred at that point?
Transcribed Image Text:(4) Obtain the differential equations associated with the following general sets of curves. If there are n constants you will need an nth order differential equation. You will first need to find the general equation of the set of curves. Some of these need quite a lot of manipulation. (a) The set of circles centred at the point (-2,3). More generally, given a fixed point (a, b), what is the equation of the first order ODE representing the set of circles centred at that point?
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