## plot 2 functions versus each other...

Hello every body i need help with my program. how can i plot r&s versus each other?

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## How can i get rid out of this error?...

restart;
with(plots); with(DEtools);
`&epsilon;` := .1;
de1 := x[0](t)+`&epsilon;`*x[1](t);
ode2 := sin(t)-`&epsilon;`*t*sin(t);
MODEL := {ode1, ode2};
VARS := {x(t), y(t)};
DOMAIN := t = 0 .. 20;
RANGE := x = -3 .. 3, y = -3 .. 3; COLORS := [BLACK, BLUE];
IC1 := [x[0](0) = 0, x[1](0) = 0]; IC2 := [(D(x[0]))(0) = 1, (D(x[1]))(0) = 0];
DEplot(MODEL, VARS, DOMAIN, RANGE, [IC1, IC2], stepsize = .1, arrows = THIN, linecolor = COLORS);
Error, (in DEtools/DEplot/CheckInitial) the 'number' option must be specified before initial conditions

## How do i plot van der pol oscillation, exact solut...

Hi, My Error is this:

DEtools; DEplot(MODEL, VARS, DOMAIN, RANGE, [IC1, IC2], stepsize = .1, arrows = THIN, linecolor = COLORS);
%;
Error, (in DEtools/DEplot) invalid range for independent variablehow can i remove error?

## struggling to use DEplot with a system of 4 differ...

Ive been trying to plot the following system

With these initial conditions (Also G*M=1)

ics:=[x(0)=1, y(0)=0,vx(0)=0,vy(0)=1];

I use this command to try and do this

with(DEtools):
DEplot(subs({G=1,M=1},satODE1),{x(t),y(t),vx(t),vy(t)},t=-2..2,ics,scene=[x(t),y(t)],scaling=constrained);

But I get this error message

Error, (in DEtools/DEplot/CheckInitial) too few initial conditions: [x(0) = 1]

Which I find odd because I have an initial condition for each variable

Im not sure what makes this different to other DE's Ive plotted other than having more equations in the system

## DEplot - Error, (in DEtools/DEplot) vars must be d...

Hello. I have a problem with DEplot and I hope someone could help me with this:

Error, More than two dependent variables, please indicate the desired scene

## How to plot a 3rd order solution curve?...

I am having touble plotting the equation, diff(y(t), t\$3)+3*(diff(y(t), t\$2))+4*(diff(y(t), t))+12*y(t) = 0. With the intional conditons y'(0)=y''(0)=0 and y(0)=3.

Currently I am getting this error, "Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem."

My current eqution is DEplot(ode, y(t), t = -1 .. 5, y(t) = -5 .. 5, [ivp]), with ivp := [((D@D)(y(t)))(0) = 0, (D(y(t)))(0) = 0, (y(t))(0) = 3].

## Asterisk tickmarks in DEplot...

I am trying to use y* to label a point on the axis of a graph made with DEplot, and am currently unable to.

with(DEtools);
NLC := diff(y(t), t) = k*(Am-y(t));
Am := 20; k := .1;
ivs := [y(0) = 10, y(0) = 30, y(0) = 50];
DEplot(NLC, y(t), t = 0 .. 20, ivs, tickmarks = [default, [20 = y^`*`]], font = [default, default, 30]);

makes y`*` apear as the label, as does the code

tickmarks = [default, [20 = y^`&ast;`]]

wheras if i remove the `` marks I get an error

## Problem with ODE...

I need to receive a plot of the next equation:

E:=0.001;

eq := E*(diff(y(x), `\$`(x, 2)))+(x^2+1)*(diff(y(x), x))-x*(x-1/2)^2 = -x^2+2.7^x ;

/*(x=0..1, y(0)=-1, y(1)=0)*/

I try to use DEplot in such way DEplot(eq, y(x), x = 0 .. 1, y = -1 .. 0); but i always get a bug like

Error, (in DEtools/DEplot) cannot produce plot, non-autonomous DE(s) require initial conditions.

## How to produce this DEplot?...

sys := {diff(b(t),t) = 0,diff(c(t),t) = -b(t)/a(t)};
DEplot(sys, [b(t),c(t)], t=0..5, x=-5..5, y=-5..5);
Error, (in DEtools/DEplot) Option keyword (x) was not in the allowed set of options, consisting of: iterations, arrows, dirgrid, obsrange, scene, colour, linecolour, stepsize, a dependent variable range, a list of initial conditions or one of the allowed plot options: {animate, axes, color, colour, coords, font, scaling, style, symbol, title, view, animatecurves, animatefield, axesfont, dirfield, labelfont, linestyle, numframes, resolution, thickness, tickmarks, titlefont, xtickmarks, ytickmarks}, or one of the allowed dsolve/numeric options: {abserr, control, ctrl, initial, itask, maxder, maxfun, maxkop, maxord, maxpts, maxstep, method, mi..

## Convergence of nonlinear oscillator...

Hello,

I have an non coupled non linear oscillator.

I notice that, if I try to plot for a time too big, my plot doesn't converge anymore and didn't keep an elliptic trajectory. In other words, the plot didn't stay in the limit cycle.

Do you know why, if tmax is too big, the solution is no longer stable ? Do you have ideas so that I can keep a stable limit cycle even if I increase tmax ?

My code is the following :

r:=sqrt((x(t)/a)^2+(z(t)/b)^2);
eqx:=diff(x(t),t)=alpha*(1-r^2)*x(t)+w*a/b*z(t);
eqz:=diff(z(t),t)=beta*(1-r^2)*z(t)-w*b/a*x(t);
EqSys:=[eqx,eqz];

params := alpha=1, beta=1, a=0.4, b=0.2, w=1;

EqSys := eval([eqx,eqz], [params]);
xmax := 0.8; zmax := 0.4;
tmax := 400;
ic:=[x(0)=0.4, z(0)=0];
DEplot(EqSys, [x(t),z(t)], t= 0..tmax, [ic],linecolor=black, thickness=1,x(t)=-xmax..xmax, z(t)=-zmax..zmax, scaling=constrained,arrows=none);

Thanks a lot for your help.

## 3D phase space with directional field...

hello guys,

i have a system of autonomous equations which i want to plot its 3D phase space with directional field,

i have some problem with it :dy.mw , and i dont know how to command for add some directional field for 3D phase space .

thank you guys

## Plot of coupled nonlinear oscillators...

Hello,

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>]);
omega[sw]:=beta/(1-beta)*omega[s];
for i to 4
do
r[i]:=sqrt((u[i](t)/(L/2))^2+(v[i](t)/H)^2):
omega[i]:=omega[st]/(1+exp(b*v[i](t)))+omega[sw]/(1+exp(-b*v[i](t))):
Equ[i]:=diff(u[i](t),t)=Au*(1-r[i]^2)*u[i](t)+omega[i]*(L/2)/H*v[i](t):
Eqv[i]:=diff(v[i](t),t)=Av*(1-r[i]^2)*v[i]+omega[i]*(L/2)/H*v[i](t)+MatrixVectorMultiply(K,<seq(v[i](t),i=1..4)>)[i]:
EqSys[i]:=[Equ[i],Eqv[i]]:
end do:

My parameters are the following:

paramsGeo:=L=0.015,H=0.015,beta=0.5,Vf=0.3;
omegaS:=eval(Pi*Vf/L, [paramsGeo]);
paramsCycle:=omega[s]=omegaS,Au=1,Av=1,b=100;
params:=paramsGeo,paramsCycle;

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

## How to use loop in Maple?...

Hello

i have an ODE like this:

I sove this ODE with plot order:

with(plots);
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:

## DEplot of elliptic nonlinear oscillator...

Hello,

I would like to plot an non linear oscillator.

The equations are the following:

r:=sqrt((x(t)/a)^2+(z(t)/b)^2);
eqx:=diff(x(t),t)=alpha*(1-r^2)*x+wa/b*z(t);
eqz:=diff(z(t),t)=beta*(1-r^2)*y+wb/a*x(t);
EqSys:=[eqx,eqz];

The constants are the following :

alpha:=1:
beta:=1:
a=0.4:
b=0.2:
w=1:

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

Thank a lot for your help and ideas

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