# Ordinary Differential Equation System with Variable Coefficients

## Homework Statement

For $$t\in\mathbb{R}$$, let:

$$A=\left[\begin{array}{ccc} -1 & 0 & 0\\ 0 & 2 & 2t\\ 0 & 0 & 2\end{array}\right]$$

Get the solution for the general equation: $$X'=A(t)X$$

## The Attempt at a Solution

I done many of these problems, all with constant coefficients, but I don't know how to do in this case.

CompuChip
$$x'(t) = f(t) x(t)$$
$$x(t) = x_0 \exp\left( \int_{t_0}^t f(\xi) \, d\xi \right)$$