Hello I need help with solving this Math Problem that deals with Differential Equations. Please show all the correct ste

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Hello
I need help with solving this Math Problem that deals with Differential Equations. Please show all the correct steps and the correct answer.
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: 4a. (1)=2x₁(1)-3x₂ (1) ₂' (t) = x₁(t)-2x₂ (1) |x (1)=2x₁ (1)+5x₂ (1) [x₂ (1)=-x₁ (1)-2x₂ (1) 4b. using the B-y method and determine the stability of the system at the origin subject to (0)=0 x₂ (0)=1 and