Second order DE in matrix form

[teapsoon]

Homework Statement

Consider the differential equation \bold{x}'=\left[ \begin{array}{cc} -1 & 2 \\ -1 & -3 \end{array} \right]\bold{x}, with \bold{x}(0)=\left[ \begin{array}{c} 1 \\ 1 \end{array} \right]

Solve the differential equation where \bold{x}=\left[ \begin{array}{c} x(t) \\ y(t) \end{array} \right].

solving for the x vector and y vector

Homework Equations

The Attempt at a Solution

 

[Mark44]

Homework Statement

Consider the differential equation $$\bold{x}'=\left[ \begin{array}{cc} -1 & 2 \\ -1 & -3 \end{array} \right]\bold{x}$$, with $$\bold{x}(0)=\left[ \begin{array}{c} 1 \\ 1 \end{array} \right]$$

Solve the differential equation where $$\bold{x}=\left[ \begin{array}{c} x(t) \\ y(t) \end{array} \right]$$.

solving for the x vector and y vector

Homework Equations

The Attempt at a Solution

I added [ tex] and [/ tex] tags (without leading spaces inside the brackets).

What have you tried? Do you have any ideas for how you might solve this system of equations?