Find the solution to the linearization around zero of the system x'=-x-4y-2x^2, y'=16x-y-xy^5. Initial conditions: x(0)=0.7, y(0)=0.8. I attempted to solve it by finding the Eigenvalues and eigenvectors, but I'm not sure what to do when I have imaginary eigenvalues. My eigenvalue is sqrt(65) and -sqrt(65).

Question

amistre64 · Answer

im not even sure how i would go about trying to solve it with eugene stuff

amistre64 · Answer

how would you set up the matrix to determine the values and vectors with?

anonymous · Answer

I just realized that I made a mistake as I was typing my response...I'll try again and see what I get. It might not be imaginary after all.

amistre64 · Answer

cool, afterwards you might be able to teach me a thing or two ;)

amistre64 · Answer

i just found out from a similar post that the order that you line up the column vectors matters ....

anonymous · Answer

I just got the signs of one of the numbers wrong.

anonymous · Answer

The eigenvalues I got were -1+16 and -1-16.