Differential equations. Stability analysis of autonomous systems with constant coefficients Given the system: x´ = ax + by y´ = cx + dy with a,b,c,d constants and b≠0. Aswer the following questions: a) In what cases can it happen that there is only one eigenvector? b) What happens to the asymptotic stability of the solution? Please argue your answers, be as clear as possible and legible. Show and explain in detail all the steps and use definitions if necessary. Thank you a lot.

Differential equations. Stability analysis of autonomous systems with constant coefficients

Given the system:

x´ = ax + by
y´ = cx + dy

with a,b,c,d constants and b≠0. Aswer the following questions:

a) In what cases can it happen that there is only one eigenvector?

b) What happens to the asymptotic stability of the solution?

Please argue your answers, be as clear as possible and legible. Show and explain in detail all the steps and use definitions if necessary. Thank you a lot.