General Solution for a 2x2 Matrix Differential Equation

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SUMMARY

The general solution for the differential equation x'=(2, 9/5, -5/2, -1)x is expressed in terms of real-valued functions derived from the complex roots (1/2)+(3/2)i and (1/2)-(3/2)i. The parameters a and b for the roots are a=1, b=(3/5)+(3/5)i for the first root and a=1, b=(3/5)-(3/5)i for the second root. The solution involves utilizing these roots to construct the general solution effectively. The user successfully solved the equation after initial uncertainty.

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Express the general solution of x'=(2, 9/5, -5/2, -1)x in terms of real-valued functions.

(this is 2x2 matrix, 2 and 9/5 on the left, -5/2 and -1 on the right. The complex roots are (1/2)+(3/2)i and (1/2)-(3/2)i and a=1, b=(3/5)+(3/5)i for the first root. And a=1, b=(3/5)-(3/5)i for the second root. But I don't know how to get the answer.
 
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Never mind. I solved it.
 

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