## How do I solve a system of differential equations ...

Hello everyone

I need help solving a system of equations as below. I'm looking for a way to do it, but I don't understand the general concept of how such an equation is calculated. So far I've been using a package in LabVIEW that worked similarly to Simulink and that was clear to me, whereas here I'm overwhelmed by the multitude of options and that's why I'm asking for help.

I need to solve these equations analogously to Matlab-Simulink, i.e., a time interval and integration step, and a numerical procedure in symbolic versions.

Help_me.mw

## Multiplaction "dot" is way too small - causes erro...

Multiplaction "dot" in Maple 2022 is way too small - causes errors.

e.g. two variables multiplied s*m ends up being sm a new variable as I cannot really see that there is a missing multiplication operator between the variables. This causes huge unnecessary errors.

Maple 9.x e.g had nice clear and big operators and this kind of error was avoided.

How can I undo this unfortunate regression in Maple 2022 to increase the size of multiplication operator and other operators, so that they actually becom visible and not just a little dot almost a pixel in size.

If I was a falcon (20x20)^infinity then this would have been ok, but I am not, I am human.

So how do I change this unfortunate regression so that these errors can be avoided.?

## integration in if-statement...

How can I get the evaluation of integration inside if-statement?

 > restart;
 > #L:=1:sigma:=0.01:beta:=0.2:k0:=-100:
 > #For Free particle Projectile := proc({L:=1,sigma:=0.01,beta:=0.2,k0:=-100},n_max) local x0,g,c:  x0:= beta*L;  g := unapply(exp(-(x-x0)^2/2/sigma^2),x);  #c := int(g(x)^2,x=-L/2..L/2,numeric=true);  ub := (L/2-x0)/sqrt(2)/sigma;  lb := (-L/2-x0)/sqrt(2)/sigma;  a := Pi*sqrt(2)*sigma/L;  b := sqrt(2)*k0*sigma;  c := Pi*x/L;  d := k0*x0;  eq1 := [cos(a*n*z)*cos(b*z)/e^(z^2),cos(a*n*z)*sin(b*z)/e^(z^2),sin(a*n*z)*cos(b*z)/e^(z^2),sin(a*n*z)*sin(b*z)/e^(z^2)];  eq1 := map(f->unapply(f,n,z),eq1);  eq2 := [cos(n*c)*cos(d),cos(n*c)*sin(d),sin(n*c)*cos(d),sin(n*c)*sin(d)];  eq2 := map(f->unapply(f,n,z),eq2);  for j from 1 to n_max do:    if (is(j,odd)) then eq11 := int(eq1[1](j,z),z=lb..ub,numeric=true);    else 0;    end if;  end do: end proc:
 >
 > Projectile(1);
 (1)
 >

## strange window behavior problem...

OS Linux

I have Maple 2022 open with a worksheet on a specific workspace.

I then move to a different workspace and want to start a new instance of maple for a new problem.

In command line I exacute

\$]xmaple22 –standalone  filename.mw

Unfortunately when the new instance is started, the open maple instance on the first workspace is moved automatically to the second workspace together with the new instance opened, completely messing up the organization.

This is not expected behavior.

How can I make Maple execute absolutely independent instances of xmaple22 without indiscressionately and automatically moving existing open maple instances to the current workspace.

Severely annoying. Maple 9.5 e.g. does not have this behavior at all so Maple 2022 is a step backwards in this regard.

Thanks

## HELP WITH A CORRUPTED FILE ASAP!...

Hey! I need help ASAP, because my maple file has been corrupted and i dont know what to do. Do you guys know how to recover a file? i can save it again as_mw. but should i change it to xml? or how? i have the link to my maple file attached, so if someone can help me, it could be helpful! Because i have an upcoming exam. Thanks youu

## How to compute right eigen vector of a matrix in ...

How to evaluate the right eigenvector of a given matrix in maple?

## how to plot impulse points in the differential equ...

For t not equal to nT,

dS/dt = delta- mu*S+ omega*V;

dV/dt = -(omega+mu)*V

For t=nT,

S(nT+)=(1-gamma) S(nT);

V(nT+)=V(nT)+ gamma* S(nT),

with the initial conditions  S(0+)=s0

V(0+)=v0

how to plot the graph with this system of equations,impulsive points and initial conditions

## how do I solve and plot fractional differential eq...

I want a maple code to solve the caputo fabrizio differential equations using Runge Kutta method with implicit functions and impulsive conditions in maple. Is there any code structure for that.

## is this correct to solve the implicit fractional d...

restart;
with(Student[NumericalAnalysis]);
with(plots);
with(DEtools);
f := proc(u, r) local res; res := 1/25*r^2 + (sin(u(r)) + sin(diff(u(r), [r \$ 1/5])))/(r^2 + 47); return res; end proc;

RK4 := proc(f, u0, r0, h, n) local u, r, i, k1, k2, k3, k4; u := Vector(n + 1); r := Vector(n + 1); u[1] := u0; r[1] := r0; for i to n do k1 := f(u[i], t[i]); k2 := f(u[i] + 1/2*h*k1, r[i] + 1/2*h); k3 := f(u[i] + 1/2*h*k2, r[i] + 1/2*h); k4 := f(u[i] + h*k3, r[i] + h); u[i + 1] := u[i] + 1/6*h*(k1 + 2*k2 + 2*k3 + k4); r[i + 1] := r[i] + h; end do; return [u, r]; end proc;
RK4 := proc (f, u0, r0, h, n) local u, r, i, k1, k2, k3, k4; u

:= Vector(n+1); r := Vector(n+1); u[1] := u0; r[1] := r0;

for i to n do k1 := f(u[i], t[i]); k2 := f(u[i]+(1/2)*h*k1,

r[i]+(1/2)*h); k3 := f(u[i]+(1/2)*h*k2, r[i]+(1/2)*h); k4 :=

f(u[i]+h*k3, r[i]+h); u[i+1] := u[i]+(1/6)*h*(k1+2*k2+2*k3+k4\

); r[i+1] := r[i]+h end do; return [u, r] end proc

u0 := cos(abs(0.9))/15;
u0 := 0.04144066455

r0 := 0;
r0 := 0

h := 0.1;
h := 0.1

n := 100;
n := 100

solution := RK4(f, u0, r0, h, n)

u := solution[1];
r := solution[2];
plot(u, r, style = line, color = blue, labels = ["Time (r)", "Solution (u)"]);
is this correct to solve the implicit fractional differential equations using 4th order Runge-Kutta Method. will fsolve command  solve the fractional differential equations ?

## looking help for streamline by using dsolve or num...

I am trying to draw the streamline for my coupled system but do not get the outcome. Could anyone please help in this regard?

Detail: My system contains x and y;  Regrading x=0, if I do not assign it to zero, do not get the results. Otherwise, there is no need to put x=0 because I am interested in plotting stream plots between y and x (y on the vertical axis and x on the horizontal axis). Besides this, I solved this system analytically, then considered the stream function, did some steps, and plotted the streamline. It is different from the stream function, which has been obtained directly by using the numeric method. I have assigned the values to the parameters that I used during the analytical plot. I put x=0 and did not get the answer. Besides,  I am uploading the graph as a reference, which I have obtained by considering the stream function. This plot is similar to my flow direction, and I expect the same results from the numeric method.

streamline_Help.mw

## expression when t goes to infinity...

I am trying to find the value of y4 at t=infinity and t=-infinity when lambda1>lambda2 or lambda1<lambda2. But every time I got the same answer. For example, if we do it by hand then the terms which are responsible for making the indeterminate form can be extracted and canceled (see Fig.).

But in limit.mw y4 is too lengthy-expression and very difficult to do it manually.

## 'n' and 'm' are real...

As I assumed 'n' and 'm' are real, eta is complex. But still, there is a bar on these discrete independent variables. Secondly, the substitution of (8) applies in some terms of 'r2', and the remaining terms remain as is it.

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## Take advantage from the SSTransformation command...

I would like to take advantage from the powerful command "SSTransformation" of the DynamicSystems package to reuse the corresponding output.

For example, if we use the following shape:

> SSTransformation( Amat, Bmat, Cmat, Dmat, form = ModalCanon, output=['A','B','C','D','T'] );

How to do to assign names to the outputs A,B,C,D and T to subsequently reuse them?

## Is this a Maple error or my system?...

Maple 2022.2

> restart
> expr = x^4-10*x^2+1
> plot(expr)

produces an error message:
com.maplesoft.maplets.ComponentAccessException: not a valid plot structure

plot(expr, x) works Ok.

Tom Dean

## Why does this error appear after simplifying?...

 > restart
 > V := m^4*(1-(varphi/mu)^p);
 (1)
 > V1 := diff(V, varphi);
 (2)
 > V2 := diff(V1, varphi);
 (3)
 > f := Zeta * (varphi^2);
 (4)
 > f1 := diff(f, varphi);
 (5)
 > f2 := diff(f1, varphi);
 (6)
 > R:= simplify(((V/3-f1*V1/(3*V))/((1-kappa^2*f)/(12*kappa^2)+f1/V)));
 (7)
 > N:=evalf(int((3*V1*kappa^2*((2*V*V1)/3 - f1^2*V1*R/(3*V) - f1*V1^2/(3*V))/(V*(-f*kappa^2 + 1)*(-R*f1 - 2*V1))),varphi=varphi__hc..varphi__end)assuming varphi__hc > 0, varphi__hc > varphi__end);
 (8)
 >