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I would like to plot an non coupled non linear oscillator.

The equations are the following:

K:=Matrix([<0, -1, 1, -1>,<-1, 0, -1, 1>,<-1, 1, 0,-1>,<1, -1, -1,0>]);
for i to 4
end do:

My parameters are the following:

omegaS:=eval(Pi*Vf/L, [paramsGeo]);

I'm not sure with my initial equations. But, may be it is possible to start with:

ic:=[u[1](0)=0.8, v[1](0)=0,u[2](0)=0.8, v[2](0)=0,u[3](0)=0.8, v[3](0)=0,u[4](0)=0.8, v[4](0)=0];

For these equations, I would like to obtain the following plots:
- plot 1: horizontal axis : u[1](t) vertical axis : v[1](t).
- plot 2: horizontal axis : u[2](t) vertical axis : v[2](t).
- plot 3: horizontal axis : u[3](t) vertical axis : v[3](t).
- plot 4: horizontal axis : u[4](t) vertical axis : v[4](t).
- plot 5: horizontal axis : t, vertical axis : v[1](t), v[2](t), v[3](t), v[4](t).

For this last plot, I would like to obtain this kind of curve:

I image that since my equations are coupled i can not use directly use Deplot function but Dsolve.

May you help me for defining a good syntax for solving my system and then deducing the following plots?

Thanks a lot for your help


i have an ODE like this:

I sove this ODE with plot order:

odeplot(sol, [x, (3*D1*a+4*D2)*P(x)/((1-q*S(x))*D2)], .5 .. (1/2)*Pi, tickmarks = [[seq((1/10)*i*Pi = (180*i*(1/10))*`°`, i = 1 .. 8)], default]);
my plot work very well. but i need to plot this ODE with five different parameter (q for for instance, q=0.1 & q=0.2 ....) all in one axis. something like this:


I would like to plot an non linear oscillator.

The equations are the following:


The constants are the following :


I didn't manage with Deplots. May you help me to plot this oscillator?

Thank a lot for your help and ideas

sys := [(diff(c(t), t))*(diff(a(t), t))*(diff(b(t), t))+(diff(c(t), t))*t^2, (diff(c(t), t))*(diff(a(t), t))*t+(diff(c(t), t))*t*(diff(b(t), t)), (diff(c(t), t))*(diff(a(t), t))*(diff(b(t), t))+(diff(c(t), t))*(diff(a(t), t))*t+(diff(c(t), t))*t^2]
DEplot(sys, [a(t), b(t), c(t)], t = 0 .. 2, a = -15 .. 15, b = -15 .. 15, c = -15 .. 15, color = magnitude, title = `Stable Limit Cycles`, arrows = curve, dirfield = 800, axes = none);
odeplot(sys, [t, a(t), b(t), c(t)], -4 .. 4, color = orange);

eq1 := a(t)*(diff(a(t), t))+a(t)*(diff(a(t), t))*b(t)*(diff(b(t), t))*c(t)*(diff(c(t), t));
eq2 := a(t)*(diff(a(t), t))+a(t)*(diff(a(t), t))*c(t)*(diff(c(t), t))+a(t)*(diff(a(t), t))*b(t)*(diff(b(t), t))*c(t)*(diff(c(t), t));

DEplot({eq1, eq2}, [b(t), c(t)], t = 0 .. 1, b = 0 .. 1, c = 0 .. 1, [[b(0) = 1, c(0) = 1]], arrows = large);

Error, (in DEtools/DEplot/CheckDE) only derivatives of dependent variables can be present

DEplot({eq1 = 3*t^2, eq2 = 2*t^3}, [b(t), c(t)], t = 0 .. 1, b = 0 .. 1, c = 0 .. 1, [[b(0) = 1, c(0) = 1]], arrows = large);
Error, (in DEtools/DEplot/CheckDE) only derivatives of dependent variables can be present



i make an attempt to plot the solution to

Here is my code :

> with(plots); with(DEtools);
> ode1 := diff(x(t), t) = v(t); ode2 := diff(v(t), t) = -(.8*9.8)*v(t)/abs(v(t))-cos(t)^2;
> MODEL := {ode1, ode2}; VARS := {v(t), x(t)}; DOMAIN := t = 0 .. 150; RANGE := x = -1 .. 1, v = -5 .. 5; COLORS := [BLACK, BLUE]; IC1 := [x(0) = .5, v(0) = .25]; IC2 := [x(0) = 2.5, v(0) = 3];
> DEplot(MODEL, VARS, DOMAIN, RANGE, [IC1, IC2], stepsize = .1, linecolor = COLORS, scene = [t, x]);

and the message cannot evaluate the solution further right of .16015784, maxfun limit exceeded (see ?dsolve,maxfun for details)

Any other attemp has failed.

Have you got somme ideas



Hi guys,

I'm trying to draw a phase portrait based on a system of differential equations, but executing the DEplot command gives me the response in the title. 

The command I entered is this one :

DEplot(sysdif,[u(t),nu(t)],t=0..50,{[u(0)=0.831,nu(0)=0.7]},linecolor=red,numpoints=1000, thickness=1, u=0.5...1, nu=0.6...1, color=black);

the system of equation is this one :

eqd1 := diff(u(t), t) = u(t)*[-gamma + (rho)/(mu - nu(t)) - delta*u(t) + pii - (tau)/(alpha + epsilon*exp(-beta*((omega-u(t))/(kappa-u(t)))))] ;
eqd2 := diff(nu(t), t) = nu(t)*[(omega-u(t))/(kappa-u(t)) - (tau)/(alpha+epsilon*exp(-beta*((omega-u(t))/(kappa-u(t)))))] ;


the model is calibrated. I understand that maple cannot store a kind of number but even changing the parameters won't help. I've been looking for people with same error message but using solutions provided by forum members don't work. Before getting that error message i did have the one with "vars must be declared as a list ..." so I did :

u:='u' ;


but now I have the error  "unable to store  '[HFloat(0.005711776872341132)]' when datatype=float[8]".

Does anybody have an idea of the solution to my problem ?

Thanks for your time,

best regards,



While I was using DEplot3d, I want to draw a space curve, the equation of which is a list of functions of the vars in DEs. I put them in "scene", but Maple told me this:

Error, (in DEtools/DEplot) Invalid scene; must be list of vars: scene = ...

Now I know that I cannot put functions in "scene", but I am wandering if there are some other way so I can draw this kind of space curve.

Thank you very much!

Use the Maple command DEplot to draw a direction field for the equation

make sure it at least covers the area −1 ≤ x ≤ 1,
−1 ≤ y ≤ 1

the equation is dy/dx+4y^3 −3y = 0.

then I have :


with(DEtools); DEplot(y(x), x = -1 .. .1, y = -1 .. .1);

Error, (in DEtools/DEplot) vars must be declared as a list, e.g. [x(t),y(t),...]


so how can I change the command to make it work..

In the attached Maple worksheet I attempt to plot the solution of an initial value problem for a first order ODE.  DEplot fails with a cryptic message.  Strangely enough, if I give the "arrows=none" option to DEplot, it produces the correct plot!

I see this behavior in Maple 17 and 18.

Maple 11, however, works fine with or without the "arrows=none" option.

Is there an explanation for this or is it a bug?

I have a DEplot :

DEplot(sys, [x(t), y(t)], t = 0 .. 30, [[x(0) = 0.8, y(0) = 0]], x = -1.25 .. 1.25, y = -1.25 .. 1.25, numpoints = 300, axes = boxed);

I would like to draw on this plot two circles centered in the origin with different radiuses.

How can I proceed?

Consider the differential equation   d/dx y(x)=2*y(x)*(y(x)-4), on the rectangle -1 < x < 1, -2 < y < 7.40 in the xy-plane.

(a) Use DEplot to plot the direction field for the differential equation on the given domain. Assign your answer to my_plot_1.

restart: with(DEtools):


DEplot(DE, y(x), x=-1..1, y=-2..7.4);
Error, (in DEtools/DEplot/CheckDE) derivatives must be given explicitly


Thanks for your help!


Use DEplot to sketch a direction field for my_deq and the solution curve for the initial condition T(0) = 88 C. Assign your plot to my_plot.

*Note: my_deq is the differential equation 


My input:


ODE2:=(Diff(T(t), t) = 1/59*(18-T(t)));

DEplot( ODE2, T(t), t=-4..4, {[T(0)=88]}, y=0..100);


Error Received: 

Error, (in DEtools/DEplot/CheckInitial) the 'number' option must be specified before initial conditions


The only thing I can find about this error is the input isn't in the form of a differential equation... But I'm pretty sure it is.


I am having trouble printing out a limit cylce on maple 16.  I have the attached file and if anybody could look at it and perhaps help me out it would be greatly appreciated.  The first limit cycle is supposed to look somewhat like the second one.  I'v tried many different things but nothing seems to be working.  an explenation would also be nice too.  if the file does not open correctly also let me know. thank you very much.

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