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### 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!

 2 None calc314 4181 ●22 ●48 ●113

### 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) 2*(-x)/sqrt(x^2+(t-y)^2)
de2 = diff(y,t) == 2*(t-y)/sqrt(x^2+(t-y)^2)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') var('t')
x = function('x',t) function('x',t)
y = function('y',t) function('y',t)
de1 = diff(x,t) == 2*(-x)/sqrt(x^2+(t-y)^2) 2*(-x)/sqrt(x^2+(t-y)^2)
de2 = diff(y,t) == 2*(t-y)/sqrt(x^2+(t-y)^2) 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)[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!