Hello I need help with solving this Math Problem that deals with a system of Differential Equations. Please show all the

[answerhappygod]

Hello
I need help with solving this Math Problem that deals with a system of Differential Equations. Please show all the correct steps and the correct answer.
Please use the eigenvalues / eigenvectors method and make sure to write everything neat and clear so I can see the work.
Also please provide the correct answer with the correct steps in complete detail and please be neat, this is very important to me, and I promise that I will rate you.
Thank you very much.
System of differential equations: Solve the following system of differential equations: E' (1)=2x, (t)-3x, (1) 3' (t)= x;(t)-2x,() using the B -y method and determine the stability of the system at the origin E' (t) = 2x,(t)+5x2(1) z) ) (t)=-x(1)-2x,(6) subject to *,(0) = 0 and *3(0)=1 Using the eigenvalues/eigenvector method and determine the stability of the system at the origin