Question: Solve the following differential system. Consider the differential system: {x^1= x 2y t, y^1=2x y 1} (S 1 ). 1. Solve the homogenous system 2.

Solve the following differential system. Consider the differential system:

{x^1= x 2y t, y^1=2x y 1} (S1).

1. Solve the homogenous system

2. Find a particular solution of the form x (t)=at b, y(t)=ct d; a,b,c,d E R

3. Give the general solution of (S1 )subject to the initial condition: x(0)=1, y(0)=2

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