# System of differential equations

Hi! I am doing a project on pursuit curves, and I am trying to plot the system:

```
de1 = diff(x,t) == 2*(-x)/sqrt(x^2+(t-y)^2)
de2 = diff(y,t) == 2*(t-y)/sqrt(x^2+(t-y)^2)
```

with *x(t)* and *y(t)* being my *i* and *j* components for the trajectory a an object.

I wrote:

```
t = var('t')
x = function('x',t)
y = function('y',t)
de1 = diff(x,t) == 2*(-x)/sqrt(x^2+(t-y)^2)
de2 = diff(y,t) == 2*(t-y)/sqrt(x^2+(t-y)^2)
f,g = desolve_system([de1, de2],[x,y],ics = [0,10,0])
show(f)
show(g)
```

It gives me a solution for my system, *x(t)* and *y(t)* (that I don't understand, since I hacen't seen Laplace), but I can't figure out how to plot the vector equation *A(t)* = *x(t)**i + *y(t)**j.

I wanted to use
**parametric_plot(x(t),y(t),(t,0,20))**
but it doesn't work.

Could anyone help me?

Thank you!