A = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}

A // MatrixForm

Eigensystem[A]

Clear[x1, x2, x3]

\(\(
DSolve[{\(x1'\)[t] == x1[t] + 2  x2[t] + 3  x3[t], 
		
        \(x2'\)[t] == 4  x1[t] + 5  x2[t] + 6  x3[t], 
				
        \(x3'\)[t] == 7  x1[t] + 8  x2[t] + 9  x3[t]}, {x1[t], x2[t], x3[t]}, 
      t]\)\)

\(Clear[x1, x2, x3]
\)\(DSolve[{\(x1'\)[t] == x1[t] + 2  x2[t] + 3  x3[t], 
		
        \(x2'\)[t] == 4  x1[t] + 5  x2[t] + 6  x3[t], 
				
        \(x3'\)[t] == 7  x1[t] + 8  x2[t] + 9  x3[t], 
	x1[0] == 0, 
        x2[0] == 2, x3[1] == 4}, {x1[t], x2[t], x3[t]}, t]\)

% // Simplify