Given the curve (x^2)y+ax+by=0 have three inflection points, where a and b are constants. a) Using implicit differentiation, find y' and y'' in terms of a and b. b) Find the values of a and b if one of the inflection points is (2, 5/2). c) With the answer in (b), find another two inflection points.
Given the curve (x^2)y+ax+by=0 have three inflection points, where a and b are constants. a) Using implicit differentiation, find y' and y'' in terms of a and b. b) Find the values of a and b if one of the inflection points is (2, 5/2). c) With the answer in (b), find another two inflection points.
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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Given the curve (x^2)y+ax+by=0 have three inflection points, where a and b are constants.
a) Using implicit
b) Find the values of a and b if one of the inflection points is (2, 5/2).
c) With the answer in (b), find another two inflection points.
Expert Solution
Step 1
We are given that the curve x2y+ax+by=0 has three inflection points, where a and b are constants.
For (a),
Using implicit differentiation, we need to find y' and y'' in terms of a and b.
Here, x2y+ax+by=0
=> y = (-ax/(x2 + b))
Step 2
So,
Further,
So,
.
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