Given the following C^1 solution (x(t),y(t)) of:

{x' = -x^3 +x*y^2

{y' = -y^3 +y*x^2

How do I show that it will not interesct a circle centered @ (0, 0) more than once?

Also, I cannot find C^1 solution in my book. What is it?

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- March 4th 2011, 09:12 AMBorkborkmathC^1 solutions intersecting circles
Given the following C^1 solution (x(t),y(t)) of:

{x' = -x^3 +x*y^2

{y' = -y^3 +y*x^2

How do I show that it will not interesct a circle centered @ (0, 0) more than once?

Also, I cannot find C^1 solution in my book. What is it? - March 4th 2011, 10:19 AMTheEmptySet
- March 4th 2011, 12:08 PMBorkborkmath
When I put

{

{

I meant that as a piecewise function, if that changes anything. I think that the professor might have typo'd the question if, as you beautifully explained it, the equation can be separated by variables.

On a side note, how do you type with all the mathematical symbols? - March 4th 2011, 12:16 PMTheEmptySet
2nd question first. It is called LaTex

http://www.mathhelpforum.com/math-help/f47/

I assume you mean parametric form. I just eliminated the parameter. If the minus sign was not there you would get a line though the origin. If there were some restriction like

or then the statement would be true.