# Graphing with Mathematica

1. Mar 28, 2007

### b2386

Hi all,

Right now I am doing some Diff equations homework but am having difficulty with a problem. The problem asks me to draw a direction field for the system $$x' = \left(\begin{array}{cc}1 & 1\\4 & 1\end{array}\right)\left(\begin{array}{cc}x_1\\x_2\end{array}\right)$$

The proper Mathematica function is of the form PlotVectorField[{f(x), f(y)},{x, xmin, xmax}, {y, ymin, ymax}], where f(x) and F(y) are the function in terms of x and y. I understand how to do this for a simple function such as $$y' -2y=4-t$$. In this case, f(x) = 1 and f(y) = 2y-t+4. However, the matrices that I am currenly facing make things for difficult. The resulting graph should have axes of x_1 and x_2 but that's all I know for sure. Can anyone help me please?

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