Hi I'm new to maple

I wanted to use dsolve to solve and equation but instead of getting an answer, maple returns an integration.

What could the promblem be?

Thanks

Hello friends,

I try to write a loop in Maple.

The equation is f (x) = x + 3

x is a variable and should be from 50 to 70 with dx = 5 can be used in the function, so that f (x) is to be determined.

How can I write such a loop?

how to solve this eq by maple:

P:=Matrix([[ 0 , .5 , .5 , 0 , 0 , 0 ], [ 1/3 , 0 , 0 , 1/3 , 1/3 , 0 ], [ 1/3 , 0 , 0 , 0 , 1/3 , 1/3 ], [ 0 , 1 , 0 , 0 , 0 , 0 ], [ 0 , .5 , .5 , 0 , 0 , 0 ], [ 0 , 0 , 1 , 0 , 0 , 0 ]]);

pii:=Vector[row]([ a , b , c , d , e , f ])

how to find

pii.P=pii

Silaws

with(combinat); 

L:=permute([1$(n*(n-1)/2), 0$(n*(n-1)/2)], n*(n-1)/2);

Error, (in combinat:-permute) 2nd argument must be a non-negative integer

what is $ in permute?

Hi,

I have a problem solving two equations.  They are as follows:

s := 1/(273.16+50); s1 := 1/(273.16+145); s3 := 1/(273.16+250); s2 := 1/(273.16+197.5); gamma0 := 0.1e-3; gamma1 := .5; gamma2 := 0.15e-2; beta := -3800:

c := 300; n := 200; tau1 := 99; tau2 := 120;

Delta := solve(1-exp(-(gam0*tau1+(1/2)*gam1*tau1^2)*exp(beta*s1)) = 1-exp(-(gam0*a+(1/2)*gam1*a^2)*exp(beta*s2)), a);
a := Delta[1];

Theta := solve(1-exp(-(gam0*(a+tau2-tau1)+(1/2)*gam1*(a+tau2-tau1)^2)*exp(beta*s2)) = 1-exp(-(gam0*b+(1/2)*gam1*b^2)*exp(beta*s3)), b);
b := Theta[1];

n1 := int((gam1*t+gam0)*exp(beta*s1)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s1)), t = 0 .. tau1);
n22 := (n-n1)*(int((gam1*t+gam0)*exp(beta*s2)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s2)), t = a1 .. a1+tau2-tau1));
n2 := eval(n22, a1 = a);
n33 := (n-n1-n2)*(Int((gam1*t+gam0)*exp(beta*s3)*exp(-(gam0*t+(1/2)*gam1*t^2)*exp(beta*s3)), t = b1 .. c));
n3 := eval(n33, a1 = a);
n4 := n-n1-n2-n3;

g1 := -n1*(Int((1/(gam1*t+gam0)-t*exp(beta*s1))*(gamma2*t^2+gamma1*t+gamma0)*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1)), t = 0 .. tau1))-n2*(Int((1/(gam0+gam1*(a+t-tau1))-(a+t-tau1)*exp(beta*s2))*(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2)*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2)), t = tau1 .. tau2))-n3*(Int((1/(gam0+gam1*(b+t-tau2))-(b+t-tau2)*exp(s3))*(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3)), t = tau2 .. c))+(n-n1-n2-n3)*(1/(gam0+gam1*(b+c-tau2))-(b+c-tau2)*exp(s3))*(gamma0+gamma1*(b+c-tau2)+gamma2*(b+c-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+c-tau2)+(1/2)*gamma1*(b+c-tau2)^2+(1/3)*gamma2*(b+c-tau2)^3)*exp(beta*s3));

g2 := -n1*(Int((t/(gam1*t+gam0)-(1/2)*t^2*exp(beta*s1))*(gamma2*t^2+gamma1*t+gamma0)*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1)), t = 0 .. tau1))-n2*(Int(((a+t-tau1)/(gam0+gam1*(a+t-tau1))-(1/2)*(a+t-tau1)^2*exp(beta*s2))*(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2)*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2)), t = tau1 .. tau2))-n3*(Int(((b+t-tau2)/(gam0+gam1*(b+t-tau2))-(1/2)*(b+t-tau2)^2*exp(s3))*(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3)), t = tau2 .. c))+(n-n1-n2-n3)*((b+c-tau2)/(gam0+gam1*(b+c-tau2))-(1/2)*(b+c-tau2)^2*exp(s3))*(gamma0+gamma1*(b+c-tau2)+gamma2*(b+c-tau2)^2)*exp(beta*s3)*exp(-(gamma0*(b+c-tau2)+(1/2)*gamma1*(b+c-tau2)^2+(1/3)*gamma2*(b+c-tau2)^3)*exp(beta*s3));

solve({g1 = 0, g2 = 0}, {gam0, gam1});

Warning, solutions may have been lost.

What do I do wrong?

Thanks for advice in advance.

Hello, I am new user of Maple and I have simple problem. I have different results after pasting and typing text. Can you help me?

I am attempting to reproduce the the direction field for the the diferential equation below that I found in a book. I am using the dfieldplot command in the window x=0..3 and y=-1..1 but Maple is only plotting the field above the x-axis. I am aware that this is neither a linear DE nor does it posses a unique solution. Is the type of DE the problem here? Do I need to use a different command?

Hi there

How can we plot the volume of revolution of r=1-cos(theta) about the line theta-pi/2 in maple13?

Regards

Yegan

I am new to Maplesoft environment. I was trying to create a nested loop as given below:

I came across this error:

                               j:=1
Error, increment of for loop must be numeric.

Could anyone kindly help?

Thanks

I'd like to know how to ask Maple to find numerical solutions to underspecified systems of nonlinear equations.  For example, suppose I had a system of equations like this:

eq1 := y1 = tanh(x1);

eq2 := y2 = cosh(x1 + x2);

eq3 := y1 + y2 = 2.0;

Typing this:

fsolve([eq1, eq2, eq3]);

results in the following error:

Error, (in fsolve) number of equations, 3, does not match number of variables, 4

In this situation I can easily artificially restrict the system to find a solution.  For example, I can do:

eq4 := x1 = 0.0;

fsolve([eq1, eq2, eq3, eq4]);

which will result in the following solution:

{x1 = 0., x2 = 1.316957897, y1 = 0., y2 = 2.000000000}

The issue here is that I pulled x1 = 0.0; out of thin air.  Setting a single variable to zero would not work to solve an arbitrary set of nonlinear equations.  How can I ask Maple to find a single (not necessarily unique) solution to an underspecified system of nonlinear equations?

Hi there,

I am trying to maximize a function given a set of values to a parameter in the function. The function is an differential equation belonging to a system of two differential equations.

I have a for loop to state different values to the parameter.

Maple yields the error:

Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

When trying to maximize the function.

Supposed that I was doing something wrong in the loop, if I reproduce the contents of the loop outside, and set a value for the parameter. If I plot the solution of the ordinary differential equation, I can see where the maximum lies.

Having plot it, the Optimizamtion:-Maximize works as expected.

However, omitting the plot has a weird effect: I only get the same result depending on the bounds I set for the Maximization:

de1 := diff(A(t), t) = r*m*(1-g)*A(t)-piecewise(t < 8, r*A(t), t >= 8, (r+k)*A(t));
de2 := diff(G(t), t) = r*m*g*A(t)-l*G(t);

ics := A(0) = 25.0, G(0) = 0.;
num := dsolve({de1, de2, ics}, {A(t), G(t)}, type = numeric, output = listprocedure, parameters = [g]);

num(parameters = [g = .15]);
val := eval(G(t), num);

# odeplot(val, [t, G(t)], t = 0 .. 100);

Maximize(val);
Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

val2 := Maximize(val);

Error, (in Optimization:-NLPSolve) cannot evaluate the solution further right of 0.17757507e-4, probably a singularity

val3 := Maximize(val(t), t = 0 .. 60);

  [10267.824035766165, [t = 8.25727747134303]]

val4 := Maximize(val(t), t = 0 .. 100);

[6.863211343195069e-9, [t = 59.84184367042171]]

The right answer is [10267.824035766165, [t = 8.25727747134303]]: Why do I get two different answers even if in that range there is only one relative maximum?

I ignore whether the way I am specifying the arguments for the Maximize function is correct. val is a procedure.

What am I missing?

Attached is the worksheet: MaplePrimes_malaria_param_variation_2.mw

Thanks,

jon

I am having issues when defining functions in a loop. First, I define the first two functions as follows (here, r(x) is a function already assigned).

f_0 := x -> r(x):

f_1 := x -> r(x)*f_0(r(x)):

Then, I define successive functions in a for loop as follows.

for i from 2 to 10 do

   f_i := x -> r(x)*f_[i - 1](r(x));

end do

The loop defines the function f_2 but compiles erroneously for f_3 which, and I do admit, relies on f_2. Does someone have an idea of how to fix this issue? Any help will be greatly appreciated. Thanks.

Aslam-u-Alikum. Hope you will be fine all.  I want to plot the follwing vector in the plan z=0 at time t=0 and A=1

v := `<,>`(VectorCalculus[`-`](VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](A, y), 1/VectorCalculus[`+`](x^2, y^2)), exp(VectorCalculus[`-`](VectorCalculus[`*`](k, t))))), VectorCalculus[`*`](VectorCalculus[`*`](VectorCalculus[`*`](A, x), 1/VectorCalculus[`+`](x^2, y^2)), exp(VectorCalculus[`-`](VectorCalculus[`*`](k, t)))), VectorCalculus[`*`](B, t))

I am waiting for your positive answer.

I am trying to alter the Virtual Solar system Maple worksheet of Yi Xie in the way that I added several objects to the eight planets and Pluto (e.g. Hale-Bopp, Sedna, 2012 VP113 etc.) and would like to adjust the array such that when zooming out and the obrit and labels overlap so that it's unreadable anymore (orbits and labels) that I can switch on and off (respectively display/not display) specific parts, e.g. the inner solar system. In the original file a single array was created from 1..18 (including 9 orbital entries and 9 label entries). What I did is to create arrays for each part of the Solar system, e.g. Inner for the planets+Pluto 1..18, an array for Hale-Bopp with an orbital entry and a label entry, so [1,2], and an array with 6 entries for 3 additional objects like Sedna, Planet X and 2012 VP113. As well as the sun, which only has a single entry as there are no orbital elements necessary and one just makes a 3dplot (I did not label it, so just one entry). All arrays are converted into lists in the end and displayed. Here is the code:

> with(linalg);

> with(plots);

> with(plottools);

> P1 := matrix([[cos(omega[j]), -sin(omega[j]), 0], [sin(omega[j]), cos(omega[j]), 0], [0, 0, 1]]); P2 := matrix([[1, 0, 0], [0, cos(i[j]), -sin(i[j])], [0, sin(i[j]), cos(i[j])]]); P3 := matrix([[cos(Omega[j]), -sin(Omega[j]), 0], [sin(Omega[j]), cos(Omega[j]), 0], [0, 0, 1]]);

> A:=matrix([[a[j]*(cos(E[j])-e[j])],[a[j]*sqrt(1-e[j]^2)*sin(E[j])],[0]]);

> R:=multiply(P3,P2,P1);

> B:=multiply(R,A);

> a := [.38709893, .72333199, 1.00000011, 1.52366231, 5.20336301, 9.53707032, 19.19126393, 30.06896348, 39.48168677, 1/0.5454e-2, 268.2509283, 532.7838156, 300];

> e := [.20563069, 0.677323e-2, 0.1671022e-1, 0.9341233e-1, 0.4839266e-1, 0.5415060e-1, 0.4716771e-1, 0.858587e-2, .24880766, .994920, .7005635, .8570973, .1];

> i := [7.00487, 3.39471, 0.5e-4, 1.85061, 1.30530, 2.48446, .76986, 1.76917, 17.14175, 89.5328, 24.01830, 11.92859, 10];

> Omega := [48.33167, 76.68069, -11.26064, 49.57854, 100.55615, 113.71504, 74.22988, 131.72169, 110.30347, 282.1476, 90.88303, 144.53190, 45];

> omega := [77.45645, 131.53298, 102.94719, 336.04084, 14.75385, 92.43194, 170.96424, 44.97135, 224.06676, 130.8038, 293.03200, 311.18311, 150];

> i := map(x→ convert(x, units, deg, rad) end proc, i);

> Omega := map(x→ convert(x, units, deg, rad) end proc, Omega);

> omega := map(x→ convert(x, units, deg, rad) end proc, omega);

> for j to 13 do omega[j] := arcsin(sin(omega[j]-Omega[j])/sin(arccos(sin(i[j])*cos(omega[j]-Omega[j])))) end do;

> x := array(1 .. 13);

> y := array(1 .. 13);

> z := array(1 .. 13);

> for j to 13 do x[j] := B[1, 1]; y[j] := B[2, 1]; z[j] := B[3, 1] end do;

> Sun := array([1]);

> Inner := array(1 .. 18); for j to 9 do Colors := [black, green, blue, red, black, yellow, green, violet, brown, aquamarine, black, black, red]; Linestyle := [solid, solid, solid, solid, solid, solid, solid, solid, solid, longdash, solid, solid, longdash]; Inner[j] := spacecurve([subs(E[j] = E, x[j]), subs(E[j] = E, y[j]), subs(E[j] = E, z[j])], E = 0 .. 2*Pi, color = Colors[j], linestyle = Linestyle[j]) end do;

> Comet := array([1, 2]); if j = 10 then Colors := [aquamarine]; Linestyle := [longdash]; Comet[1] := spacecurve([subs(E[j] = E, x[j]), subs(E[j] = E, y[j]), subs(E[j] = E, z[j])], E = 0 .. 2*Pi, color = Colors[j], linestyle = Linestyle[j]) end if;

> Oort := array(1 .. 6); for j from 11 to 13 do Colors := [black, black, red]; Linestyle := [solid, solid, longdash]; Inner[j] := spacecurve([subs(E[j] = E, x[j]), subs(E[j] = E, y[j]), subs(E[j] = E, z[j])], E = 0 .. 2*Pi, color = Colors[j], linestyle = Linestyle[j]) end do;

> Sun[1] := plot3d(0.1e-1, 0 .. 2*Pi, 0 .. Pi, style = PATCHNOGRID, coords = spherical, color = red);

> Inner[10] := textplot3d([subs(E[1] = 0, x[1]), subs(E[1] = 0, y[1]), subs(E[1] = 0, z[1]), "Mercury"]); Inner[11] := textplot3d([subs(E[2] = 0, x[2]), subs(E[2] = 0, y[2]), subs(E[2] = 0, z[2]), "Venus"]); Inner[12] := textplot3d([subs(E[3] = 0, x[3]), subs(E[3] = 0, y[3]), subs(E[3] = 0, z[3]), "Earth"]); Inner[13] := textplot3d([subs(E[4] = 0, x[4]), subs(E[4] = 0, y[4]), subs(E[4] = 0, z[4]), "Mars"]); Inner[14] := textplot3d([subs(E[5] = 0, x[5]), subs(E[5] = 0, y[5]), subs(E[5] = 0, z[5]), "Jupiter"]); Inner[15] := textplot3d([subs(E[6] = 0, x[6]), subs(E[6] = 0, y[6]), subs(E[6] = 0, z[6]), "Saturn"]); Inner[16] := textplot3d([subs(E[7] = 0, x[7]), subs(E[7] = 0, y[7]), subs(E[7] = 0, z[7]), "Uranus"]); Inner[17] := textplot3d([subs(E[8] = 0, x[8]), subs(E[8] = 0, y[8]), subs(E[8] = 0, z[8]), "Neptune"]); Inner[18] := textplot3d([subs(E[9] = 0, x[9]), subs(E[9] = 0, y[9]), subs(E[9] = 0, z[9]), "Pluto"]); Comet[2] := textplot3d([subs(E[10] = 0, x[10]), subs(E[10] = 0, y[10]), subs(E[10] = 0, z[10]), Hale-Bopp]); Oort[4] := textplot3d([subs(E[11] = 0, x[11]), subs(E[11] = 0, y[11]), subs(E[11] = 0, z[11]), "2012 VP113"]); Oort[5] := textplot3d([subs(E[12] = 0, x[12]), subs(E[12] = 0, y[12]), subs(E[12] = 0, z[12]), "Sedna"]); Oort[6] := textplot3d([subs(E[13] = 0, x[13]), subs(E[13] = 0, y[13]), subs(E[13] = 0, z[13]), "Planet X ?", color = red]);

> Sun1 := convert(Sun, 'list');
> Inner1 := convert(Inner, 'list');
> Comet1 := convert(Comet, 'list');
> Oort1 := convert(Oort, 'list');
> display(Sun1, Inner1, Comet1, Oort1, scaling = CONSTRAINED);

 

The first error message appears after the if-condition. Can you tell me where I am making a mistake? Beware: when copy paste the code from Maple to Word and from Word in here the colons at the end of lines have changed into semi-colons. Hope this is no problem in executing the code despite the lines being in the same ">..." e.g. where the labels are defined.

Good day everyone, could you please help use Gauss Elimination method for these system of equations. See the worksheet here F1.mw

Thanks.