## Thomas Richard

Mr. Thomas Richard

## 3496 Reputation

14 years, 134 days
Maplesoft Europe GmbH
Technical professional in industry or government
Aachen, North Rhine-Westphalia, Germany

## Conversion to trig representation...

Typically, I would recommend evalc as well, but you may also use

`convert(exp(I*x),'trig');`

if you find that more readable.

## MapleSim and its FMI Connector...

If so, please try the "tunable" parameters in the FMI Connector App (section Parameters). Note that these are supported by FMI 2.0 Co-Simulation only.

Its functionality is also available at the Maple API level via FMIConnector:-GenerateCode.

Whether they can be accessed from Python / PyFMI, I don't know.

## DEtools:-singularities...

If you just want to obtain the results (unlike the steps), simply call

```ode := x*(x^2-9)^2*diff(y(x),x\$2) + (x+3)*diff(y(x),x) + 5*y(x) = 0;
DEtools:-singularities(ode);```

Its help page also gives definitions.

## Explicit solutions...

I am not sure if this odetest message is to be expected.

However, if we add the 'explicit' option to dsolve, the solutions are much longer, but can be handled by odetest:

```sol := [dsolve(ode,y(x),[dAlembert],explicit)]:
length~(sol);
odetest~(sol,ode);```

This takes a while (about two minutes on my office laptop).

## If you are looking for the command, that...

If you are looking for the command, that's gcdex:

```f := 54*x^3-54*x^2+84*x-48:
g := -12*x^3-28*x^2+72*x-32:
gcdex(f,g,x,'d1','d2');
d1, d2;
d1*f+d2*g;
expand(%);
```

## Both are possible...

I must admit that I did not know this ODE before, so looked it up at https://en.wikipedia.org/wiki/Chebyshev_equation.

[Always interested in learning something new!]

If that's the one you have in mind, it's very easy to obtain both closed-form solution and series expansions:

```cde := (1-x^2)*diff(y(x),x,x)-x*diff(y(x),x)+p^2*y(x)=0;
sol := dsolve(cde,y(x));
odetest(sol,cde); # optional check
ssol := dsolve(cde,y(x),'series');
odetest(ssol,cde,'series'); # optional check```

Is that what you expected?

Notice that I did not assume anything about the parameter. No convergence checks either.

## Both observations are correct: that you ...

Both observations are correct: that you can install on two computers and that you get an error message upon trying the second activation. The simple reason is that only one is enabled by default.

## Maple is available for Windows, Linux an...

Maple is available for Windows, Linux and macOS; please see its System Requirements for details.

For iOS and Android devices, we have the Maple Calculator, formerly called Maple Companion App.

## DEtools:-remove_RootOf...

You may apply remove_RootOf, which is available in the DEtools package. Please see its help page first.

But it essentially just delivers the implicit solution that dsolve would return with the 'implicit' option:

```ode:=diff(y(t),t)=-(4/3)*(a/eta)*(y(t)^3+1):
ivp:=[ode,y(0)=1]:
lambdaI:=dsolve(ivp,y(t),'implicit');
odetest(lambdaI,ivp);
lambdaE:=dsolve(ivp,y(t),'explicit');
odetest(lambdaE,ivp);
remR:=DEtools:-remove_RootOf(lambdaE);
odetest(remR,ivp);
simplify(24*a*lambdaI-remR);```

## More examples...

Maple recognizes many power series, but note that for some you need option 'formal':

```sum((-1)^n*x^(2*n)/(2*n)!,n=0..infinity);
sum((-1)^n*x^(2*n+1)/(2*n+1)!,n=0..infinity);
sum(x^(2*n)/(2*n)!,n=0..infinity);
sum(x^(2*n+1)/(2*n+1)!,n=0..infinity);
sum((-1)^n*x^(n+1)/(n+1),n=0..infinity,formal);
sum((-1)^n*x^(2*n+1)/(2*n+1),n=0..infinity,formal);
sum(x^(2*n+1)/(2*n+1),n=0..infinity,formal);```

This recognition is not restricted to elementary functions:

```convert(BesselJ(3,x),FPS);
value(%);```

Sometimes a simplification is required afterwards:

```convert(erf(x),FPS);
value(%);
simplify(%);```

## In the solve call, replace det(C) with D...

In the solve call, replace det(C) with Determinant(C).

Please see ?examples,LinearAlgebraMigration for more hints.

## Two hints...

This question received no answer yet, but it is a very valid one, and it is good that you are asking before installing the new OS!

First of all: when a new major version of an OS appears, you must expect problems with existing applications. Yes, in an ideal world all OS developers would care about backwards compatibility. Reality is very different from that. Even minor version updates can break compatibility, as you have experienced. (This affects all mainstream OS families: Mac OS, Windows, and Linux, just in varying degrees over time.)

AFAIK, the beta version of the new Mac OS is currently under investigation by our developers. Once Maple, MapleSim, etc. have been adapted and tested successfully, we will publish that accordingly.

Simple advice: if you are running Maple 2020 under a currently supported OS (such as Mac OS 10.13 - 10.15), wait with upgrading the OS until the applications have been tested. There is no time pressure to upgrade the OS once its vendor releases a new version.

## First, there is a * character (multiplic...

First, there is a * character (multiplication symbol) missing in front of the (1/x) factor. Better simply divide by x, and you can omit some parentheses:

`int((cosh(a*x)-1)/sinh(b*x)/x,x=0..infinity) assuming b>abs(a);`

But even with correct input, it returns unevaluated, i.e. int is not yet capable of completing G&R 3.529.

## Contact Customer Service...

The best option is to contact custservice@maplesoft.com, as explained at https://www.maplesoft.com/support/. Please describe the problem and include your Purchase Code.

Do not post any Purchase Codes on MaplePrimes or other public places.

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