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I have a system of differential equations:

enter image description here

The problem I have to solve is the following:

Draw the vector space of the system using matlab in a rectangle containing the stationary points.For $t\in[0,10]$ make animation of the movement of the point $(x(t),y(t))$ which at time $t=0$ starts from point $(x_1,y_1)$ which is enetered with the mouse by clicking in on the rectangle.

What does draw the vector space mean? Does it mean I have to solve for $x$ and $y$ in terms of $t$ and then draw the graphic?

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The topic you want to known is called phase portrait.

See for instance this post about phase portrait of ODEs with MATLAB$^®$.

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As pointed out by Jack, you will want to plot a phase portrait for the dynamical system.

If you are not required to write the program yourself, then consider getting the program PPLANE.

You can find the program here:

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