8.3.38 Systems of Ordinary Differential Equations

Condition: Find a private solution to the system of differential equations that satisfy the specified initial conditions: \ [\ begin {array} {l} \ frac {d x} =-2 x-4 y, \ quad \ frac {d t} = 5 x+7 y \\ x (0) = 1, = 1, = 1, = 1, = 1, \ quad y (0) = 1 \ end {array} \]