MaplePrimes Questions

Dear all
I have a boundary value problem, 
How can I solve the problem using maple or maybe we can introduce serie expansion to solve it or something else.

BVP_frac.mw

Thank you for your help 

I have problem to calculate the max value for 3d  phase potret for each period. Thank You

 deplot3d-animated_SIA.mw

How could one reduce this equation int(x^2*diff(y(x), x)/(x^2 - 1), x) = int(y(x)^(1/2), x)^(-2/3)down to a first order ordinary differential equation? Maple can solve this equation, namely, 9*(1/x^(5/3) - 1/x^(11/3))*x*(sqrt(y(x))*x)^(8/3)/(8*(x^2 - 1)) - 3*x*(4*x^2 - 1)*(1/x^(5/3) - 1/x^(11/3))/(8*(x - 1)*(x + 1)) + _C1 = 0 , however I could not understand how this equation was arrived at, leading me to go to 'odeadvisor', which responded with y = G(x,y'(x)) labelled as the 'patterns' method, which appears to require a first order ode - that is why I raised the reduction question.

Please pardon the poor format below.  I'm new to Maple and cannot figure out how to cut and paste worksheet code which includes  Maple prompts.  

I would like to create a list of funtions in a set and then select one and plot its real or imaginary surface.  I'm able to do this with a single function below:

h := z -> z^(1/2);
    h := proc (z) options operator, arrow; z^(1/2) end proc

plot3d(Im(h(x + y*I)), x = -1 .. 1, y = -1 .. 1);

This plots the Imaginary surface of z^(1/2).  However I need to do this with a set of functions delimited with curly brackets such as:

functionList = {2 + z, z^2 - 3*z, -z^3 + 4};
                          /        2          3    \ 
          functionList = { 2 + z, z  - 3 z, -z  + 4 }
                   \                        / 

And if I now try and select the first function in functionList and attempt to plot it, the plot is blank.

v := z -> functionList[1];
v := proc (z) options operator, arrow; functionList[1] end proc

plot3d(Im(v(x + y*I)), x = -1 .. 1, y = -1 .. 1);
Warning, expecting only range variables [x, y] in expression Im(functionList[1]) to be plotted but found name functionList[1]

 Can someone help me with this problem and also explain to me how to format this post nice like the others?

Thanks for reading.

I wanted to solve a pde of two variables in spherical coordinates with a boundary condition at a specific radius. I am doing something wrong because the pdsolve just evaluates for several minutes and does not actually give anything.

Could someone have a look and let me know what I am doing wrong.

restart

``

with(Physics[Vectors])

Setup(mathematicalnotation = true)

[mathematicalnotation = true]

(1)

eq3 := Laplacian(Phi_out(r, theta)) = 0

((r^2*(diff(diff(Phi_out(r, theta), r), r))+2*r*(diff(Phi_out(r, theta), r))+diff(diff(Phi_out(r, theta), theta), theta))*sin(theta)+(diff(Phi_out(r, theta), theta))*cos(theta))/(r^2*sin(theta)) = 0

(2)

bc1 := eval(Phi_out(r, theta)-Omega*mu*(-1+cos(2*theta))/(2*r), r = R) = 0

Phi_out(R, theta)-(1/2)*Omega*mu*(-1+cos(2*theta))/R = 0

(3)

``

pdsolve([eq3, bc1])

NULL

Download laplacian.mw

Hi,

How to generate different letters? I've tried the 'exclude' option, which doesn't work in this context. Thank you.QuestionAlphabet.mw

I have data that I've binned in list. I'd like to plot in as a histogram. 

dataplot sort of does it but doesn't give the x-axis that I used but just the bins.

Yes, I know about Histogram from Statistics. To plot 1000000 values I have to enter them all into a list which seems crazy when all I want is a 100 bin histogram. Doing the binning is trivial, but I can't figure out how to plot it with a sensible x-axis (show range used to define the 'histogram')

Hi,

I want to provide my students with a series of exercises involving radicals, but I don't want the final simplification to display rational exponents. I only want a solution in simplified form with radicals. Ideas? Thanks

QRadicaux.mw

how to make a phaseportrait curves with animation? so i can see how the curve going on. Thank you

caring_phase_pemanenan_predator_dgn_parametersesuai_jurnal.mw

Hello,

I am experiencing difficulties using my old Maple programs with the newer version. I tried changing the types of inputs and the typesetting level, but it just doesn't work. I would appreciate it if someone could help me overcome my ignorance.

Some simple input is attached with the output.

Hi everyone, I am trying to draw bar graph for my expression, but received error. Could anyone please help me in this regard.

Help_Bar_graph.mw

Hi

On the latest Maple 2022 version, using dsolve with 1st order ODE and Dirac function returns an incorrect solution

dsolve({D(y)(t) + y(t)/tau = Dirac(t)/tau, y(0) = 0})

See attached image. The correct impulse response should be :

y(t) = exp(-t/tau)*Heaviside(t)/tau

The returned solution is 0 for t = 0 and scaled by a 1/2 for t > 0. I never had such an issue with older Maple versions. Is this a bug or am I doing something wrong

Here is the expected solution followed by the Maple solution:

Hi,

I use the RamdonGraph function quite a bit and wanted to know if it is possible to generate random graphs with specific properties, beyond the typical order, size, connectednes, etc. Specifically, I am interesting in generating eulerian (containing an eulerian circuit), semi-eulerian (containing an eulerian trail) and hamiltonian (containing a spanning cycle)  graphs. Also, the abiltiy to randomly generate graphs that have none of these properties would be helpful.

How do I find the contents of a bin in a Maple histogram?

hello,

I computed some algebraic calculation, but near point -1 there is some issue like disconvergencies. Can anyone help in this regard? In the final graph, as seen the paths of the curves are close together and convergence does not occur AROUND POINT -1.

restart

Digite := 30

30

(1)

beta := 2.5; lambda := 0.1e-1; b := Pi; a := Pi; alpha := 0; y[1] := 1.5; y[2] := 1.5; x[1] := -1; x[2] := 1; Q[1] := 40; Q[2] := 35; T[1] := 20

2.5

 

0.1e-1

 

Pi

 

Pi

 

0

 

1.5

 

1.5

 

-1

 

1

 

40

 

35

(2)

v := (2*n-1)*Pi/(2*b)

Delta := exp(2*v*a)*(alpha*v+beta)*(1+lambda)-(1-lambda)*(alpha*v-beta)

omega := Pi/(2*b)

P[1] := ((1+lambda)*exp(-v*abs(x-xi))+(1-lambda)*exp(v*(x+xi)))*exp(2*v*a)+(1+lambda)*exp(-v*(x+xi))+(1-lambda)*exp(v*abs(x-xi))

P[2] := ((1+lambda)*exp(-v*abs(x-xi))+(1-lambda)*exp(v*(x+xi)))*exp(2*v*a)-(1+lambda)*exp(-v*(x+xi))-(1-lambda)*exp(v*abs(x-xi))

P[3] := P[1]*(-alpha^2*v-alpha*beta+alpha*v)+beta*P[2]

G[11] := (sum((alpha*P[1]*(1-lambda)*(alpha*v-beta)*exp(-2*v*a)+(1+lambda)*P[3])*(cos(v*(y-eta))-cos(v*(y+eta)))/(v*(exp(2*v*a)*(alpha*v+beta)*(1+lambda)-(1-lambda)*(alpha*v-beta))), n = 1 .. 80))/(2*b*(1+lambda))+(2*(1+lambda)*alpha*b/Pi*.25)*ln((1+2*exp(-omega*abs(x-xi))*cos(omega*(y-eta))+exp(-2*omega*abs(x-xi)))*(1-2*exp(-omega*abs(x-xi))*cos(omega*(y+eta))+exp(-2*omega*abs(x-xi)))*(1+2*exp(-omega*(2*a+x+xi))*cos(omega*(y-eta))+exp(-2*omega*(2*a+x+xi)))*(1-2*exp(-omega*(2*a+x+xi))*cos(omega*(y+eta))+exp(-2*omega*(2*a+x+xi)))/((1-2*exp(-omega*abs(x-xi))*cos(omega*(y-eta))+exp(-2*omega*abs(x-xi)))*(1+2*exp(-omega*abs(x-xi))*cos(omega*(y+eta))+exp(-2*omega*abs(x-xi)))*(1-2*exp(-omega*(2*a+x+xi))*cos(omega*(y-eta))+exp(-2*omega*(2*a+x+xi)))*(1+2*exp(-omega*(2*a+x+xi))*cos(omega*(y+eta))+exp(-2*omega*(2*a+x+xi)))))/(2*b*(1+lambda))+(2*(1-lambda)*alpha*b/Pi*.25)*ln((1+2*exp(omega*(x+xi))*cos(omega*(y-eta))+exp(2*omega*(x+xi)))*(1-2*exp(omega*(x+xi))*cos(omega*(y+eta))+exp(2*omega*(x+xi)))*(1+2*exp(-omega*(2*a-abs(x-xi)))*cos(omega*(y-eta))+exp(-2*omega*(2*a-abs(x-xi))))*(1-2*exp(-omega*(2*a-abs(x-xi)))*cos(omega*(y+eta))+exp(-2*omega*(2*a-abs(x-xi))))/((1-2*exp(omega*(x+xi))*cos(omega*(y-eta))+exp(2*omega*(x+xi)))*(1+2*exp(omega*(x+xi))*cos(omega*(y+eta))+exp(2*omega*(x+xi)))*(1-2*exp(-omega*(2*a-abs(x-xi)))*cos(omega*(y-eta))+exp(-2*omega*(2*a-abs(x-xi))))*(1+2*exp(-omega*(2*a-abs(x-xi)))*cos(omega*(y+eta))+exp(-2*omega*(2*a-abs(x-xi))))))/(2*b*(1+lambda))

g[12] := lambda*((alpha*v+beta)*exp(v*(2*a+x))+(alpha*v-beta)*exp(-v*x))*exp(-v*xi)/(v*Delta)

G[12] := (sum(g[12]*(cos(v*(y-eta))-cos(v*(y+eta))), n = 1 .. 80))/b

phi[1] := int(int(G[11]*Q[1]*Dirac(xi-x[1])*Dirac(eta-y[1]), xi = -a .. 0), eta = 0 .. b)+int(int(G[12]*Q[2]*Dirac(xi-x[2])*Dirac(eta-y[2]), xi = 0 .. infinity), eta = 0 .. b)

Z[1] := diff(phi[1], x)

psi[1] := int(Z[1], y)

plot3d(psi[1], x = -a .. 0, y = 0 .. b)

 

with(plots)

contourplot(psi[1], x = -a .. 0, y = 0 .. b)

 

 

Download sai_1.mw

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