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
Question

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.

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

Advanced Math homework question answer, step 2, image 1

So, 

         Advanced Math homework question answer, step 2, image 2

Further,

Advanced Math homework question answer, step 2, image 3

So, 

Advanced Math homework question answer, step 2, image 4.

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