## How to write the sequence...

This is a simple model of the covid infection as it applies here, down under, without the use of any de's like

https://www.mapleprimes.com/posts/212100-Exploring-The-CoVid19-Outbreak

I'm told a substantial number of people do recover within 45 days ....
So on the 45th day 1 person has recovered, on day 50 two people have recovered and so on.

Just want to know how to write this sequence...

Covid_dbling.mw

## How do I solve an unknown that makes a bivariate p...

I have a bivariate polynomial in x,y,say P, and a parameter, say d, appears in P. I want to find d for which P has at least one non trivial factor. Is there  a fats way to do this in maple. Any help would be appreciated.

## Changing terms to be a function...

Hi,

I am struggling to find a way to change a term like x to x(t) automatically. If I have something like

```Data := x^2

diff(Data, x);
```

the result is 2x

How can I change this 2x to be 2x(t)?

Thanks,

Baharm31

## Solving simultaneous ODEs...

Hi guys,

I am trying to find x(t) from these two equations:

```odeA := m*diff(x(t), t, t) = -m*A*sin(2*Pi*f*t) - k*x(t) + 0.5*q(t)*(N__f*epsilon__0*L*(-2*x(t)/(G^2 - x(t)^2) + 2*(G__1^2 - x(t)^2)*x(t)/(G^2 - x(t)^2)^2)*(G^2 - x(t)^2)/(2*tan(alpha)*(G__1^2 - x(t)^2)) + N__f*epsilon__0*L*(-2*x(t)/(G^2 - x(t)^2) + 2*(G__2^2 - x(t)^2)*x(t)/(G^2 - x(t)^2)^2)*(G^2 - x(t)^2)/(2*tan(alpha)*(G__2^2 - x(t)^2)))/(N__f*epsilon__0*L*ln((G__1^2 - x(t)^2)/(G^2 - x(t)^2))/(2*tan(alpha)) + N__f*epsilon__0*L*ln((G__2^2 - x(t)^2)/(G^2 - x(t)^2))/(2*tan(alpha)) + C__p) - d*diff(x(t), t);

diff(q(t), t) = (q(t)/(N__f*epsilon__0*L*ln((G__1^2 - x(t)^2)/(G^2 - x(t)^2))/(2*tan(alpha)) + N__f*epsilon__0*L*ln((G__2^2 - x(t)^2)/(G^2 - x(t)^2))/(2*tan(alpha)) + C__p) + V__bias)/R1

```

How can I use dsolve to find x(t), apart from q(t) all other parameters are constant.

Thanks,

Baharm31

## Why Maple pdsolve still unable to solve 1D convect...

Can one hope that next version of Maple will be able to solve the standard convection-diffusion pde in 1D?

`pde:=diff(u(x,t),t)=d*diff(u(x,t),x\$2)+c*diff(u(x,t),x);`

in 1D. Even the most simple form with zero boundary conditions can't be solved.

```pde:=diff(u(x,t),t)=d*diff(u(x,t),x\$2)+c*diff(u(x,t),x);
bc:=u(0,t)=0,u(L,t)=0;
ic:=u(x,0)=f(x);
sol:=pdsolve([pde,ic,bc],u(x,t)) assuming d>0,c>0,L>0

sol := NULL```

I tried some HINT's also but not all of them.

FYI, Mathematica 12.1 is now able to solve the above PDE

```ClearAll["Global`*"];
pde=D[u[x,t],t]==d*D[u[x,t],{x,2}]+c*D[u[x,t],x];
bc={u[0,t]==0,u[L,t]==0};
ic=u[x,0]==f[x];
DSolve[{pde,bc,ic},u[x,t],{x,t},Assumptions->{d>0,c>0,L>0}]```

Gives Is it possible I am overlooking some other option or a trick to obtain solution for the above using pdsolve? Only reason I am asking is that Maple can solve much more complicated PDE's and the above is one of the basic diffusion based PDE's. So I am surprised why Maple still can't solve this as it is just a seperation of variables method.

Maple 2020 on windows 10. Physics version 631

## implicit plot of function...

Why is my figure not smooth? How can I make it smooth?    ## Whose minimum value is more reliable？...

I have a problem about extremal function.

The function is shown below with restricted condition of x and a:  x>=2 and -1 < a <0.

(x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)

I guess that  it's minimum value is greater than 0.  In other words,  I want prove that  (x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)>0

when I use Minimize function,

Optimization:-Minimize((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a),{x>=2, -1<a, a<0})

I 'm not seeing but Error, (in Optimization:-NLPSolve) strict inequalities are not valid constraints. I cannot but add the condition of equality of a : -1<=a, a<=0.

Optimization:-Minimize((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a),{x>=2, -1<=a, a<=0})

A result is returned with a warning:
Warning, no iterations performed as initial point satisfies first-order conditions
[0.000000, [a = -2.225074*10^(-308), x = 2.000000]]

Local or Global ?

When I read recent question post

https://www.mapleprimes.com/questions/229132-Maximize-Function-Does-Not-Work?ref=Feed:MaplePrimes:New%20Questions

I'm worrying  that Maple only returns local  extremun. So I use the freely  maple package DirectSearch. We can get it from  https://www.maplesoft.com/applications/view.aspx?SID=101333.

DirectSearch:-GlobalOptima(-((x-3/2)^a-(x-1)^a+(1-2^(a-1))*((x-3/2)^a-(x-1/2)^a)-x*((x-3/2)^a+x^a-(x-1/2)^a-(x-1)^a)),{x>=2, -1<a, a<0},maximize);

Note: I add a  minus sign to find maximize value .

It returns: [0.002264, [a = -0.000203, x = 1.019590*10^13], 605]

But I substitute the value of a and x  into the function，it returns strange result:   4078.360000 not  -0.002264.

I’m confused..

I try to use  Mathematica,

NMinimize[{(x - 3/2)^a - (x - 1)^
a + (1 - 2^(a - 1))*((x - 3/2)^a - (x - 1/2)^a) -
x*((x - 3/2)^a + x^a - (x - 1/2)^a - (x - 1)^a),
x >= 2 && a > -1 && a <= 0}, {x, a}]

It retruns {0., {x -> 13.256, a -> 0.}}  May be well.

mimimize.mw

## Tables and plots in Maple...

i need to create a table with information from plots like how many times x become 0

this is the way to make an null oscillation

## how do I integrate HeunB function with complex arg...

I am trying to calculate the following integra
r*rr*g1^2*h1^2*f1^2*fh1^2*exp(-2*t)/t

here g1 is a kummerM functin in s, and also h1 is another kummerM function  in ss, and f1 and fh1 are the HeunB functions with complex arguments in r and rr. and t=sqrt((r-rr)^2+(s-ss)^2).I would like to integte over dr drr ds dss

## how to represent a recurent suite...

restart; F := rsolve({16*s(n+1) = 2+12*s(n)-2*s(n-1), s(1) = 1, s(2) = 5/8}, s); Error, (in s) cannot determine if this expression is true or false: n

## How to solve system of equation without Rootof...

solve({sigma*E-(mu+alpha+gamma)*I = 0, gamma*E+Lambda*N*P-(mu+alpha)*R = 0, Beta__1*S*E+Beta__2*S*I/(I*M+1)-(mu+sigma)*E = 0, Lambda(1-p)*N-mu*S-Beta__1*S*E-Beta__2*S*I/(I*M+1) = 0}, {E, I, R, S}, explicit)

## Maximize function does not work...

I'm not sure if there's something on the page I'm not seeing but even  https://www.maplesoft.com/support/help/Maple/view.aspx?path=Optimization/Minimize#examples

 Maximize(2*x^2 + 2*y^2 + y, {2*x + y <= 6, y^2 - x <= 2})

a literal copy-paste of the posted example maple just repeats what I posted Idk whats wrong. btw is there some way to read the maple documentation pages?

## Naming variables/formula's...

Wis_BS2_Taak2_2019-2020_20200323-1.mw

Hello,

I have some huge troubble with making sure all formula's wont be forgotten by Maple.

For example:

f(x):=a+b;
a:=5;
b:=2;
f(x):=f(x);  --> gives me f(x):=f(x) instead of saying f(x):=7

In my document the naming is a bit more complex.

I have a variable named "M_Inwendig2[y]" in the uploaded document. When i name it "M_Inwendig2(y)" (notice [-->( )
maple refuses to use the previous filled/calculated variables.

Due to this error i have copy and pasted the answer to a new formula to continue my work, therefor it becomes quite messy... Now i am trying to fix this.

Ideal all names will be M[inwendig2](y). So the first letter will tell the kind of variable (Moment) the subscript will tell the part (inside) and the depending variable will be between ().

In the document i have marked all error's and copy's RED.

Anyone can advice me? i have named variables the same way in the past, but now it doesnt work.

Regards,

## Difficulty in Creating a Post...

I had difficulty in making my latest post.  It would fail at Submit.

I had success when I saved a draft post.  I was able to edit the draft to submit.

Lee

## Ease of Manipulating Formulae in Maple...

I am interested in how easy it is to work with formulae in the Maple language.  For example, you can easily add two equations together with '+'.

 > e1:=x^2+1=2*x; (1)
 > e2:=x^3+x=5; (2)
 > e1+e2; (3)

I was pleased when the following example added (x+1) to both sides of an equation,

 > e3:=x+1; (4)
 > e1+e3; (5)

Some other algebraic operations work.

 > e1-e3; (6)
 > e1*e3; (7)
 > e1/e3; (8)
 > e1^(1/2); (9)

Build-in functions do not work, though, but there is a simple solution.

 > exp(e1);
 > exp(rhs(e1))=exp(lhs(e1)); (10)
 > map(exp,e1); (11)

The methods also apply to inequality formulae.  I'm not as pleased about how it does '*' and '/' for inequalities.  You can get more control using rhs and lhs functions.  Here are some examples:

 > e4:=x^3<5*(x+1); (12)
 > e4+e3; (13)
 > e4-e3; (14)
 > e4*e3; (15)
 > e4/e3; (16)
 > eval(%,x=4); (17)
 > evalb(%); (18)
 > (16)/x^2; (19)
 > simplify(%); (20)
 > lhs(e4)/e3/x^2 < rhs(e4)/e3/x^2; (21)
 > simplify(%); (22)
 >