I'm having trouble finding the eigenvalue for a given graph; but more specifically I can't seem to find the characteristic polynomial. My book tells me that the characteristic polynomial of a simple graph with n vertices is the determinant of the matrix (A-\lambdaI), where A is the adjaceny...
Do you mean when y=1?
If so then all you have to do is plug back in y in the orignal equation and solve for x. And then plug in both x and y into your final differential equation. I think that the final slope will then be -9/2.