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I'm having trouble plotting the velocity and acceleration vectors of the following space curve (r3).

May anyone help guide me in the right direction to solve this problem?

var('t')
r3(t) = (cos(t/2), sin(t), t/6)
v3 = diff(r3(t),t)
a3 = diff(v3,t)
curve3 = parametric_plot3d(r3(t),(t,0,4*pi),thickness=0.5)
velvecs = Graphics()
accvecs = Graphics()
for k in range(9):
    velvecs += arrow(r3(k*pi/2),r3(k*pi/2)+v3(k*pi/2),color='red') #Line 26
    accvecs += arrow(r3(k*pi/2),r3(k*pi/2)+a3(k*pi/2),color='blue')
show(velvecs+accvecs+curve3,axes=False)

var('t') r3(t) = (cos(t/2), sin(t), t/6) v3 = diff(r3(t),t) a3 = diff(v3,t) curve3 = parametric_plot3d(r3(t),(t,0,4pi),thickness=0.5) velvecs = Graphics() accvecs = Graphics() for k in range(9): velvecs += arrow(r3(kpi/2),r3(kpi/2)+v3(kpi/2),color='red') #Line 26 accvecs += arrow(r3(kpi/2),r3(kpi/2)+a3(k*pi/2),color='blue') show(velvecs+accvecs+curve3,axes=False)

Yes, sorry for the lack of clarity, but I'm meaning to plot the solutions of de1 and de2 at the same time. Thank you for the link.

I need to plot two differential equations on the same set of axes (with a legend showing which is which).

My domain has to be 0 ≤ t ≤ 100.

Listed below is my code, any help is greatly appreciated.

t = var('t')
x = function('x')(t)
y = function('y')(t)
de1 = diff(x,t) == -3/20*x + 1/12*y
de2 = diff(y,t) == 3/20*x-3/20*y
sol = desolve_system([de1,de2],[x,y],ics=[0,4,0])

f(t) = sol[0].rhs()
g(t) = sol[1].rhs()

I found my error, must have been an extra parenthesis somewhere.

Here is the code

x,t = var('x,t')
plot1 = plot_slope_field(5*x-.3*x^2-2(1+cos(pi*t)),(t,0,10),(x,0,20),headaxislength=3,headlength=3,axes_labels=['$Time$','$Fish Pop.$'],title="No Harvesting",fontsize=13)
x = function('x')(t)
soln = lambda c:desolve_rk4(diff(x,t)==5*x-.3*x^2-2(1+cos(pi*t),x,ics=[0,c],end_points=[0,10],ivar=t,step=0.1)
plot2 = lambda c, color:list_plot(soln(c),plotjoined=True,axes_labels=['$Time$','$Fish Pop.$'],thickness=2,color=color)
show(plot1+sum(plot2(c,color=tuple(colormaps.hsv(1-c/13)[:3])) for c in [1,3.25,5.5,7.75,10]),ymin=0,ymax=20)

File "<ipython-input-27-1dec6aa982e7>", line 6
    plot2 = lambda c, color:list_plot(soln(c),plotjoined=True,axes_labels=['$Time$','$Fish Pop.$'],thickness=Integer(2),color=color)
        ^
SyntaxError: invalid syntax

*The carrot was pointing at the "2" of "plot2"

Please help.

Here is some code

x,t = var('x,t')
plot1 = plot_slope_field(5*x-.3*x^2-0*t,(t,0,10),(x,0,20),headaxislength=3,headlength=3,axes_labels=['$Time$','$Fish Pop.$'],title="No Harvesting",fontsize=13)
x = function('x')(t)
soln = lambda c:desolve_rk4(diff(x,t)==5*x-.3*x^2-0*t,x,ics=[0,c],end_points=[0,10],ivar=t,step=0.1)
plot2 = lambda c:list_plot(soln(c),plotjoined=True,axes_labels=['$Time$','$Fish Pop.$'],thickness=2)
show(plot1+plot2(12),ymin=0,ymax=20)

Referencing the last line of code, I wish to input .1, 3, 6, 9, and 12 all at the same time.

x,t = var('x,t') plot1 = plot_slope_field(5x-.3x^2-0t,(t,0,10),(x,0,20),headaxislength=3,headlength=3,axes_labels=['$Time$','$Fish Pop.$'],title="No Harvesting",fontsize=13) x = function('x')(t) soln = lambda c:desolve_rk4(diff(x,t)==5x-.3x^2-0t,x,ics=[0,c],end_points=[0,10],ivar=t,step=0.1) plot2 = lambda c:list_plot(soln(c),plotjoined=True,axes_labels=['$Time$','$Fish Pop.$'],thickness=2) show(plot1+plot2(12),ymin=0,ymax=20)

Referencing the last line of code, I wish to input .1, 3, 6, 9, and 12 all at the same time.