For this integro-differential equation,

Equation:= int[y'(x)* (x^2)/[(x^2)-1],x)  =  (int[sqrt(y(x)])^(-2/3)

Maple is able to obtain an exact intrinsic solution

from which an exact solution can be extracted, namely,

ExtrinsicSolution:= y(x) = sqrt(3)*(-8*_C1*x^(8/3) + 12*x^2 - 3)^(3/4)

My question concerns how was this solution obtained.

Even more, specifically, 'odeadvisor' suggests converting the

equation in question to the form

ode:= y = G(x,diff(y(x),x));

However, I cannot reconcile how this can be applied to an equation which

contains two integrals. (Regretably, I am not able to directly, attach my

Maple worksheet directly on to this sheet). The situation is that after

applying 'dsolve' to the above 'Equation', Maple comes back with an

intrinsic solution which can was used to obtain the 'ExtrinsicSolution' in 

the above.  So it is the missing steps between applyingthe dsolve command

to Equation and the intrinsic solution which MS provides which, in turn, leads

to the 'Extrinsic Solution' above. I would greatly, appreciate if anyone can 

fill in the missing steps.

How to convert barycentric coordinates to cartesian ? Thank you

Is there a way to manipulate an equation so that it is in the form of (Expression of Primary Variables)*(Expression of Secondary Variables)
In the example below from Video 1: Fast Analytical Techniques for Electrical and Electronic Circuits (youtube.com), the primary variables are R1 and R2

PS. When I type ctrl-v to insert an image, I always get 2 copies.

I got the proportional symbol to work once, typing "proportional" + CRTL + Space.  Went for wlak came back and could not get it to work at all.

Does it actually work or am I imagining things?

Greetings All,

This is an application for control theory, specifially using Maple to solve control problems in the area of Interconnection and Damping Assignment Passivity Based Control (IDA-PBC).

- Assuming two variables (iL and Vo), there is a potential function that I am trying to solve for called "Ha".  I have two equations here, and I want to solve for Ha using the pdsolve() command:  

eq1 := diff(Ha(iL, Vo), iL) = rhs(result[1]);
eq2 := diff(Ha(iL, Vo), Vo) = rhs(result[2]);
pdsolve( {eq1, eq2  } );

Once I do this, Maple gives me an expression for Ha that has arbitrary functions in it (I understand where these are coming from).  So far, so good.

--> In order to get help solving for these arbitrary functions, I also want to tell Maple some constraints.  For example:

"the Hessian matrix of Ha must be positive definite"

Is there a way to do this?

Certainly a standard question.

I have an integer n*n matrix A (the entries are explicitly integers; there is no variable -type x- in the matrix). I want the Smith normal form of A, that is A=UDV where U,V are integer matrices with determinant +-1 and D is a diagonal matrix with -eventually- some zero and positive integers d_i s.t. d_i divides d_{i+1}.

"SmithForm()" doesn't work directly (I get rational -non integer- matrices). Maybe it is necessary to declare the matrix A as 'Matrix(integer)' ...
Thank you in advance for your help.

Has anybody been able to get Maple working on macOS Sonoma 14.4. I know it's not supported yet, but I thought there might be someone who has solved the issue with the app crashing immediately after startup.

How can a variable roller ensure that the nip is within the arc of contact between the web and the roller? Every time I run the simulation, it keeps failing.

point(A, xA, yA);
point(B, xB, yB);
point(C, xC, yC):
L3 := linestyle = 3
triangle(Tr, [A, B, C])
line(AP, [A, P]);
line(BP, [B, P]);
line(CP, [C, P]);
dr := draw([Tr(t3), AP(cbl, L3), BP(cbl, L3), CP(cbl, L3)]),
textplot([[coordinates(A)[], "A"], [coordinates(B)[], "B"], [coordinates(C)[], "C"]], align = {above, right});
display({dr, ellip}, scaling = constrained, axes = none, view = [-1 .. 14, -1 .. 11]);
Why doesn’t Maple show me the expected effect ? Thank you.

How do  I solve system of differential equations in finite difference method or finite element method?

eq1 := (diff(f(x), x, x, x))*(a*beta*f(x)^2-1)+(diff(f(x), x))^2-2*a*beta*f(x)*(diff(f(x), x))*(diff(f(x), x, x))+(diff(f(x), x))*(M+k[1])-(diff(f(x), x, x))*f(x)-(alpha*theta(x)+delta*phi(x))/rho = 0;

eq2 := -(diff(theta(x), x, x))*K[SB]*(Df-(Rd+k[hnf]/k[bf])/Pr)+N[t]*K[SB]*(diff(theta(x), x))^2-N[b]*(diff(theta(x), x))*(diff(phi(x), x))-(diff(f(x), x))*(diff(theta(x), x))-lambda*theta(x)-mu*Ec*(M*(diff(f(x), x))^2+(diff(f(x), x, x))^2) = 0;

eq3 := diff(phi(x), x, x)+Le*Sr*(diff(theta(x), x, x))+Le*f(x)*(diff(phi(x), x)) = 0;

ics := f(0) = 0, (D(f))(0) = 0, theta(0) = 1, phi(0) = 1;

bcs := (D(f))(100) = 0, theta(100) = 0, phi(100) = 0;

Parameters1 := rho = 2063.905, k[hnf] = .29942, k[bf] = .2520, mu = .38694, a = .1, beta = 5, k[1] = 2.0, M = 10, alpha = 20, delta = 20, K[SB] = .5, Df = 3, Pr = 1.2, Rd = 5, N[t] = 1.2, N[b] = 1.0, lambda = 1.5, Ec = 5, Le = .1, Sr = .1;

dS := -beta*S*Q;
dQ := Q*S*beta - Q*alpha;
dR := alpha*Q;
beta := 0.2;
alpha := 0.1;
S0 := 0.8;
Q0 := 0.2;
R0 := 0;
RungeKutta := proc(f::list, y0::list, t0::float, tf::float, h::float) local n, t, y, k1, k2, k3, k4, i; n := 1 + floor((tf - t0)/h); t := Vector(n, fill = 0); y := Matrix(n, length(y0), fill = 0); t[1] := t0; y[1] := Vector(y0); for i to n - 1 do k1 := Vector(map(f, t[i], y[i])); k2 := Vector(map(f, t[i] + 1/2*h, y[i] + 1/2*h*k1)); k3 := Vector(map(f, t[i] + 1/2*h, y[i] + 1/2*h*k2)); k4 := Vector(map(f, t[i] + h, y[i] + h*k3)); y[i + 1] := y[i] + 1/6*h*(k1 + 2*k2 + 2*k3 + k4); t[i + 1] := t[i] + h; end do; [t, y]; end proc;
f = [dS, dQ, dR];
t0 := 0;
tf := 50;
h := 0.1;
result := RungeKutta(f, [S0, Q0, R0], t0, tf, h);
t_values := result[1];
S_values := result[2][() .. (), 1];
Q_values := result[2][() .. (), 2];
R_values := result[2][() .. (), 3];
plots:-display(plot(t_values, S_values, color = "blue", legend = "Susceptible"), plot(t_values, Q_values, color = "red", legend = "Infected"), plot(t_values, R_values, color = "green", legend = "Recovered"), legend = ["Susceptible", "Infected", "Recovered"], title = "Simulation of Infectious Disease Model", xlabel = "Time", ylabel = "Population", view = [0 .. tf, 0 .. 1]);
Warning, (in RungeKutta) `i` is implicitly declared local
                         dS := -0.2 S Q

                     dQ := 0.2 S Q - 0.1 Q

                          dR := 0.1 Q

                          beta := 0.2

                          alpha := 0.1

                           S0 := 0.8

                           Q0 := 0.2

                            R0 := 0

RungeKutta := proc (f::list, y0::list, t0::float, tf::float, 

   h::float) local n, t, y, k1, k2, k3, k4, i; n := 1+floor((tf-\

  t0)/h); t := Vector(n, fill = 0); y := Matrix(n, length(y0), 

   fill = 0); t[1] := t0; y[1] := Vector(y0); for i to n-1 do 

   k1 := Vector(map(f, t[i], y[i])); k2 := Vector(map(f, 

   t[i]+(1/2)*h, y[i]+(1/2)*h*k1)); k3 := Vector(map(f, 

   t[i]+(1/2)*h, y[i]+(1/2)*h*k2)); k4 := Vector(map(f, t[i]+h, 

   y[i]+h*k3)); y[i+1] := y[i]+(1/6)*h*(k1+2*k2+2*k3+k4); 

   t[i+1] := t[i]+h end do; [t, y] end proc

[-0.2 S Q, 0.2 S Q - 0.1 Q, 0.1 Q] = [-0.2 S Q, 0.2 S Q - 0.1 Q, 

  0.1 Q]

                            t0 := 0

                            tf := 50

                            h := 0.1

Error, invalid input: RungeKutta expects its 3rd argument, t0, to be of type float, but received 0
                     t_values := result[1]

               S_values := result[2][() .. (), 1]

               Q_values := result[2][() .. (), 2]

               R_values := result[2][() .. (), 3]

Warning, expecting only range variable result[2][(NULL) .. (NULL),1] in expression result[1] to be plotted but found name result[1]
Warning, expecting only range variable result[2][(NULL) .. (NULL),2] in expression result[1] to be plotted but found name result[1]
Warning, expecting only range variable result[2][(NULL) .. (NULL),3] in expression result[1] to be plotted but found name result[1]
Error, (in plots:-display) unexpected options: [xlabel = "Time", ylabel = "Population"]

I want to center align all the math in my document. I have not been able to find a shortcut key for alignment, and I cannot find a default setting for alignment anywhere. I don't want to mouse click every single time.

Please help, thanks!

Howdy,

I am trying to do explicit Lie algebra computations, and I am not sure the best way to automate these.

Suppose I have a Lie algebra with basis e1 through e8, and I have some linear functions:

f(e1,e2) = c1e1+c2e2+...+c8e8

Now suppose I want to compute something like

[e5, f] - f([e5,e1],e2) + f([e5,e2],e1), or more generally x.f with the typical module structure.

I can do this line by line - say [e5,e1] = -e1 and [e5,e2] = 0, then I can ask Maple for LieBracket(e5,f)+f(e1,e2)-0. However, I'd like to make an operator that does this for me. Can anyone please point me in the right direction?

Thanks!

Good day. 

I recently constructed a Maple model using an LPSolve routine to solve for a classic factory (Operations Research) assignment problem. Basically, this involves 4 factories that, in any combination, can supply goods and fulfil demand to 10 customers. If any given factory is activated, the model determines what factory should supply what customer so that the weighted-distance is minimized.

However, in addtion to this - I would like to know the quantity of items that each factory supplies to each of their respective customers and I would like to verify that the quantity demanded by each customer is fulfilled. 

I was hoping that somebody could guide me on how to do this. Any suggestions would be most welcomed.

The model is attached.

Thanks for reading!

MaplePrimes_Jan_27.mw

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