Charging a capacitor with a DC is well known and interaction with a sinusoidal signal is known to perfection.

The mathematical solutions behind an arbitrary waveform V1(t) is hard or impossible? to find .

To simplify, the arbitrary wave can be expressed with a 2-d degree polynom. This gives a fairly simple

expression with an integral. The problem however is that V2(t) - the capacitor voltage - appears on both sides and maple seems unable to resolv this into a symbolic expression.

If this can be solved it would be great ! The solution should be of the symbolic form V2(a,b,c,V2start,t1,t2,RC) and give the answer what voltage the capacitor V2 would reach arter charging between t1 and t2  with a V1(t) that is changing during charge.

How do I plot the complex function |z+1||z-1|=1 in Maple? I know there is complexplot but don't quite understand how to use it.

Why Maple gives different looking solution when calling  

dsolve(sys);

vs.

dsolve(sys,deps);

? Both solution are actually correct. But look different.  Here is an example

restart;
sys:=[
diff(x(t),t) = 2*x(t)-z(t), 
diff(y(t),t) = 2*y(t)+z(t), 
diff(z(t),t)=2*z(t),
diff(w(t),t)=-z(t)+2*w(t)];
deps:=[x(t),y(t),z(t),w(t)];

dsolve(sys);

dsolve(sys,deps);

Notice the difference:

In first case, the x(t) and y(t) solutions have 2 constants of integrations, and in the second case, they have 3 constants of integration.

If we solve this using the matrix exponential method, the solution comes out to match the first one:

A:=Matrix([[2,0,-1,0],[0,2,1,0],[0,0,2,0],[0,0,-1,2]]):
sol:=Vector([x(t),y(t),z(t),w(t)])=LinearAlgebra:-MatrixExponential(A,t).Vector([_C1,_C2,_C3,_C4]);
simplify(sol)

Again, both solution verify to 0, using odetest, and I assume now it is correct (have no reason to think odetest is not correct).

But I'd like to understand more why when passing the unknowns to dsolve, the solution comes out different looking (3 constants of integrations, vs. two in this case). Should the solution be the same looking in both cases? 

This came out, since I thought my solution was wrong, since it did not look like Maple's. 

Maple 2020.1

In a recent question, the solution involved [...]::[list$3].

H:= proc(n, x, y)
    if n=0 then y+1
    elif n=1 and y=0 then x
    elif n=2 and y=0 then 0
    elif y=0 then 1
    elif not [n,x,y]::[nonnegint$3] then 
        'procname'(n-1, x, 'procname'(n, x, y-1))
    else
        thisproc(n-1, x, thisproc(n, x, y-1))
    fi
end proc

Where is  the  form [...]::[list$3] documented?

Hi all,

There is issue with saving big numbers to txt file on WIndows

Please look at the file:

txt_issue.mw

Function save just cutting a big number.

Thank you.

Hello everyone. I want to know how I can extract terms from a multivariate polynomial with the following 2 conditions:

1. It should have the lowest sum of the degree of x and of y; and
2. deg(x) - deg(y) should be either 0 or -1.

For instance, if I've f(x) = 100x^2y^2 + 35yx + 45x, I want an output of 35yx (not 45x; even though degree sum is 1, less than 2).

On the other hand, if I've g(x) = 13x^2y^2 + xy^2 + 2yx^2, I want an output of xy^2 (not yx^2 also).

In the worksheet below, variable x can be returned to type name after being assigned a value , but concatenated variable name A||1 cannot. Is there a way to return a concatenated variable to type name after it has been assigned a value, so it can be re-used as an unknown in solve commands?

Concatenate_Question.mw

 How do I write procedure for maxima minima and inflection point? F(x)=e^x^2 – e x^2 + 1 

P__eff := (4.881726014*10^(-13)*(x__1^2 + 0.3)*R/((1 - x__1)*(3*x__1^2 + 0.6)*(7.654218526*10^(-21)*R^2*(x__1^2 + 0.3)/((1 - x__1)*(3*x__1^2 + 0.6)) + 1)))*1000;
expr := eval(P__eff(R));
plot([seq(expr, x__1 = [0.3, 0.5, 0.7])], R = 10000000 .. 10000000000000, legend = [seq('x__1' = x__1, x__1 = [0.3, 0.5, 0.7])], color = ["blue", "red", "gold"], thickness = 3, axes = "boxed", gridlines = true, labels = [R, P__eff], axis[1] = [mode = log]);

Obviously, there is a problem with the logarithmic function curve in the interval of 10^7 to10^10. Can anyone tell me how to solve it？thank you very much！

I was trying to solve single variable nonlinear equation in maple. It gives reliable solution. For example,  equation of the type, solve(x cos(theta) -(2500-x (^3) sin(theta))^(1.3)-40, x).

But I wanted to solve for different values ( theta, k) simultaneously (shown below ):

Solve (x cos(theta) -(2500-x (^3) sin(theta))^(0.45)-k , x).

Where say , theta: 1,2,3,....,90

And , k: 3.1,3.2, 3.3,.............3.90

It would be great if you could provide link for some tutorials to do so. I am searching but still could not figure perfect tutorial to do so. 

I am interested to learn the procedure to solve this type of problem.

Thank you, stay safe and stay healthy. 

I'd like to plot phase plot of 2 first order ode's (along with 2 eigenvectors on same plot).

When using DEtools:-dfieldplot, the labels on the axis are not at the end, so hard to see them. Along with all the arrows, they become even harder to see.

Is it possible to have these labels (y,x) be at the ends of the axis so they are more easily seen? Here is an example below.

restart;
ode:=[diff(x(t),t) = 2*x(t)-y(t), diff(y(t),t) = 3*x(t)-2*y(t)]:
p1:=DEtools:-dfieldplot(ode,[x(t),y(t)],t=-2..2,x=-4..4, y=-4..4,arrows=SLIM,color=coral):
p2:=plot(3*x,x=-4..4,y=-4..4,color=magenta):
p3:=plot(x,x=-4..4,y=-4..4,color=blue):
plots:-display([p1,p2,p3]);

I looked at help, plot options, but do not see how to do it so far. I can change the font of the label and the font size, but I want to change the location to be at the end.

Maple 2020.1

I'm using Maple 2020 in Linux (Ubuntu 20.04). The screen resolution is 2560×1440, so I have system-wide setting of 200% scaling for all apps, but unfortunately Maple doesn't adopt the system setting and UI elements are tiny. To make it tolerable, in "Tools - Options - Interface", I've set Default Zoom to be 200% and checked the box "Large toolbar icons". However, menus (File, Edit, View etc.) and dialog boxes are still tiny.

Am I right that the Maple GUI is written in Java / Swing? I've heard that Java 9 has better support for high dpi scaling. Does the default Maple installation use Java 9?

I am porting some code I have  from Mathematica to Maple. 

In Mathematica, there is a command https://reference.wolfram.com/language/ref/CopyDirectory.html  which copies directory tree (i.e. the directory and everything below it) to a new location on the file system.

I looked at FileTools, and the Copy command there only works on files, not Directories.

"An exception is raised if source is a directory."

There must be a command in Maple to do this basic operation, but I am not able to find it. I googled.

Note: I do not want to rename the directory, but to copy it.

I could ofcourse work around this by writing code or calling system, but I would expect Maple to have a command for this somewhere.