Solve the homogeneous system 20 5 60 15 with the initial va

Solve the homogeneous system

$\"\\mathbf{X}\'(t)$

$\"\\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\$	20	5	$\"\\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\$
60	15

$\"\\mathbf{X}(t)\"$ ,

with the initial value

$\"\\mathbf{X}(0)$

$\"\\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\$	6	$\"\\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\$
-10

lnx=205t +c1 lny=6015t+c2 putting the given condition we get c1=ln6 c2=ln10 X(t)=[6e^205t] [-10e^6015t]