Thomas Richard

Mr. Thomas Richard

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11 years, 216 days
Maplesoft Europe GmbH
Technical professional in industry or government
Aachen, North Rhine-Westphalia, Germany

MaplePrimes Activity


These are answers submitted by Thomas Richard

It‘s easy to confirm Maple‘s result:

d := diff(u,x);
simplify(d);
kernelopts(platform);

 

Here's another way, in case you don't want to use the method option:

B := sqrt((-4*u^(1/3)+1)*u^(4/3));
A := 1/(-12*u+3*u^(2/3)-3*B);
eA := evala(A);
ieA := int(eA,u);
combine(ieA,'symbolic');

For algebraic numbers or functions, evala is always recommended.

Just wrap the result into square brackets (list delimiters):

b := [SearchAll("-", a)];

Insert this between restart and the calculations:

assume(c>0,r>0,v>1);

I have not tested whether this is the minimal set of assumptions - please check.

... like this:

f := x -> sqrt(-x^2+20*x);
plot(f(x),x=0..20,scaling=constrained);
ieqn := 2*Pi*Int(f(x)*sqrt(1+diff(f(x),x)^2),x=0..h)=1005;
ceqn := combine(ieqn,'symbolic');
veqn := value(ceqn);
sol := solve(veqn,h);
evalf(sol);

There is also a SurfaceOfRevolution command in the Student:-Calculus1 package, but in this case, the elementary steps are more useful.

I'm not going to do all the work (weekend is coming!), but for a start, I have demonstrated the first part: getting rid of the old linalg stuff. Also made some adjustments, minor simplifications here and there. See attached worksheet: Reduced-conical-equation-part1.mw

For more hints on that topic, see the built-in documentation by entering ?examples,LinearAlgebraMigration.

You should be able to form the equation then. Replace evalm and matrix accordingly.

The error message is pretty clear, I think. Your system contains three unknown functions (aka dependent variables), but only two PDEs. So you will need to provide one more PDE. Initial and/or boundary conditions do not count in this context.

You just need to supply the list of new variables as the 3rd argument (named newvars in the documentation):

ode := dchange(tr1,PDE,[xi,U(xi)]);

However, the ODE obtained is different from what you expected...

It seems your PDE is missing the square of u(x,t) that have in the typeset formula.

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

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

if you find that more readable.

I suppose you are asking about MapleSim and not Simulink, right? ;-)

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.

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.

Edit: added assignment to ode.

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'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(%);

 

 

 

Just add the showlabels=false option to your DrawGraph call.

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