Items tagged with equation equation Tagged Items Feed

Dear all;

I need your help to get all the solution of this nonlinear  system  with four parameters: r1, r2, q1, q2  assumed to be positives. Let the system:

the first equation is: r1*x*(1-x/q1)=x*y/(1+x)

the second equation: r2*y*(exp(-y)-q2)=-x*y/(1+x)

How can get the positive solution ( x, y) of the previous system.

Thank you for your help.

Hello people in mapleprimes,

I want to solve the next system of equation for B/A and C/A.

eq1:=A+B=F+G;
eq2:=k*(A-B)=kappa*(F-G);
eq3:=F*exp(I*kappa*a)+G*exp(-I*kappa*a)=C*exp(I*k*a);
eq4:=kappa*F*exp(I*kappa*a)-kappa*G*exp(-I*kappa*a)=k*C*exp(I*k*a);


But, though it is well-known, solve({eq1,eq2,eq3,eq4},{B/A,C/A})
does not work well, as the values I want to solve it for are
expressions: B/A and C/A not variables.

Then, you might thing the next works well.
eq:=subs({B=A/t,C=A/u},{eq1,eq2,eq3,eq4}):
solve(eq,{t,u});

But, this doesn't work well, with the answer was
only the ratio of t and u expressed as the following:

t = t, u = exp(I*k*a)*(exp(-I*kappa*a)*k^2-exp(I*kappa*a)*k^2-exp(-I*kappa*a)*kappa^2+exp(I*kappa*a)*kappa^2)*t/(4*kappa*k*exp(I*kappa*a)*exp(-I*kappa*a))

Isn't there nice way to solve the above system of equation, except that
sol1:=solve({eq3,eq4},{F,G});assign(sol1);
sol2:=solve({eq1,eq2},{A,B});assign(sol2);

Best wishes
taro

hello, i went solve these equation ,with a & b take any value

b*x*ln(x)-x*ln(a)+a=0

thank you

Solving equation...

November 17 2014 Dmitry 10

Hello all,

I have the following equation:

N*exp(-(1/2)*eta*epsilon*(N*alpha*epsilon*w+2*N*w*C[max]-alpha*epsilon*z-2*Q1*alpha)/(w*N))*S1*upsilon*w-N*S1*upsilon*w+K1^2*alpha*eta*z*epsilon+K1*alpha*eta*z*epsilon*S1 = 0

in which I need to find solution for epsilon (analytical solution) when epsilon>0.  

Thanks,

Dmitry

 

I have a nonlinear system with 4 equations and 4 unknowns. I am using fsolve. I know that there are multiple solutions for each variable but am only getting one. I need the others. what do I do??

This is my code:

R__1 := Matrix([[1, 0] , [0, 1] ]);

R__2 := Matrix([[1/2, sqrt(3)/2] , [-sqrt(3)/2, 1/2] ]);

R__3 := Matrix([[-1/2, sqrt(3)/2] , [-sqrt(3)/2, -1/2] ]);

R__4 := Matrix([[-1, 0] , [0, -1] ]);

R__5 := Matrix([[-1/2, -sqrt(3)/2] , [sqrt(3)/2, -1/2] ]);

 

d__1 := Vector( [ 0, 5.4] );

d__2 := Vector( [ 6.4, 4.539] );

d__3 := Vector( [ 11, 4.078] );

d__4 := Vector( [ 15.5, 2.079] );

d__5 := Vector( [ 19, 1.039] );

 

a := Vector( [ a__x, a__y] );

 

A__1:=R__1.a+d__1;

A__2:=R__2.a+d__2;

A__3:=R__3.a+d__3;

A__4:=R__4.a+d__4;

A__5:=R__5.a+d__5;

 

OO:=Vector([O__x,O__y]);

 

DA1:=A__2.A__2-A__1.A__1-2*(A__2-A__1).OO;

DA2:=A__3.A__3-A__1.A__1-2*(A__3-A__1).OO;

DA3:=A__4.A__4-A__1.A__1-2*(A__4-A__1).OO;

DA4:=A__5.A__5-A__1.A__1-2*(A__5-A__1).OO;

 

fsolve({DA1,DA2,DA3,DA4},{a__x,a__y,O__x,O__y});

Thanks for any tips you may be able to offer

 

What’s the simplest way to solve an algebraic equation in the complex domain?

 

For example,

 

I*(a+3*b)+2*b+5*a = 3+2*I

 

where a and b are real numbers.

 

 

I'm trying to solve a series of equations and then graph them. I'm trying to solve for the variables involved:

values := solve({eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9,

eq10, eq11, eq12, eq13, eq14, eq15, eq16}, {a, b, b, c, d, e, f,

g, h, i, j, k, l, m, n, o, p});

 

. . . but it gives me this:

Warning, solving for expressions other than names or functions is not recommended. 

values := 

  Given this equation:       (chi^2*(xi^2-1)^2+1-Omega^2)*(xi^2-Omega^2)-xi^2 = 0

   chi^2=1/1200;  I want to plot xi vs Omega. Can anyone help me out?

Hi!

I am new to Maple and have a problem I've been struggling with all day.

I have a pendulum and need to find a equation of motion in the y-direction. Please find my code in the picture below.

I can see that my problem starts at Eqy where the differentiation deletes one of the right-hand-side parts because I don't have any function y(t), and Maple thinks y(t) a constant (?)
Can somebody please tell me what I'm doing wrong?

 

Thank you in advance!


Hello,

I have been trying to compute the analytical solution of two dimensional diffusion equation with zero neumann boundary conditions (no-flux) in polar coordinates using the solution in Andrei Polyanin's book. When I use 2d Gaussian function as initial condition, i cannot get the result. If I use some nicer function like f(r,phi)=1-r; there is no problem.  

Any idea why this happens? or any suggestion to compute the analytical solution?

Thanks!

HB 

M := Matrix([[3.83170597020751, 7.01558666981561, 10.1734681350627, 13.3236919363142, 16.4706300508776], [1.84118378134065, 5.33144277352503, 8.53631636634628, 11.7060049025920, 14.8635886339090], [3.05423692822714, 6.70613319415845, 9.96946782308759, 13.1703708560161, 16.3475223183217], [4.20118894121052, 8.01523659837595, 11.3459243107430, 14.5858482861670, 17.7887478660664], [5.31755312608399, 9.28239628524161, 12.6819084426388, 15.9641070377315, 19.1960288000489], [6.41561637570024, 10.5198608737723, 13.9871886301403, 17.3128424878846, 20.5755145213868], [7.50126614468414, 11.7349359530427, 15.2681814610978, 18.6374430096662, 21.9317150178022], [8.57783648971407, 12.9323862370895, 16.5293658843669, 19.9418533665273, 23.2680529264575], [9.64742165199721, 14.1155189078946, 17.7740123669152, 21.2290626228531, 24.5871974863176], [10.7114339706999, 15.2867376673329, 19.0045935379460, 22.5013987267772, 25.8912772768391], [11.7708766749555, 16.4478527484865, 20.2230314126817, 23.7607158603274, 27.1820215271905]]):

c := 10:

A := 5:

w := proc (r, phi, t) options operator, arrow; int(int(f(xi, eta)*G(r, phi, xi, eta, t)*xi, xi = 0 .. 5), eta = 0 .. 2*Pi) end proc:

with(plots):

Warning,  computation interrupted

 

``



Download 2d_soln.mw

Hi there,

 

I'd like to solve 7th order implicit simultaneous equation such as below, so I tried to do it by solve command.

However the calculation wasn't over although three hours passed.

 

eq1 := f1(a,b,c,d,e,f,g) = 0;

eq2 := f2(a,b,c,d,e,f,g) = 0;

.

.

.

eq7 := f7(a,b,c,d,e,f,g) = 0;

 

Just for your information, the eq1 and eq6 are written as follows specifically.

eq1 := -a-b-c-d-e-f-g+0.501857 = 0

eq6 := a*b*c*d*e*f+a*b*c*d*e*g+a*b*c*d*f*g+a*b*c*e*f*g+a*b*d*e*f*g+a*c*d*e*f*g+b*c*d*e*f*g+a*b*c*d*e+a*b*c*d*f+a*b*c*d*g+a*b*c*e*f+a*b*c*e*g+a*b*c*f*g+a*b*d*e*f+a*b*d*e*g+a*b*d*f*g+a*b*e*f*g+a*c*d*e*f+a*c*d*e*g+a*c*d*f*g+a*c*e*f*g+a*d*e*f*g+b*c*d*e*f+b*c*d*e*g+b*c*d*f*g+b*c*e*f*g+b*d*e*f*g+c*d*e*f*g-0.5281141885e-3+1.01894577*10^(-12)*I = 0

 

And the program code I used is:

solve([eq1,eq2,eq3,eq4,eq5,eq6,eq7],[a,b,c,d,e,f,g]);

 

Here is the specification of my computer.

OS: Windows 7 Enterprise 64bit

CPU: Intel Core i7-3520M 2.90 GHz

Memory: 4.00 GB

 

How can I handle this problem? Is the specification not enough to solve the equation? Do I need to leave my computer more and more time?

Any help would be appriciated.

Hi there. 

I'm kind of new to Maple and i'm trying to solve a Linear Algebra problem for my class of Linear Algebra of the course of Physics. Also, my first language is portuguese so forgive for my not-so-perfect english.

I have a (solved) linear system of 7 equations and 12 variables (A, B, C, D, E, F, G, H, I, J, K, L) that is the following:

  • A = 33 - K - L
  • B = 1 + F - J
  • C = -15 - F + J + K + L
  • D = 15 + H - K
  • E = 16 - F - H + J + K
  • G = 34 - H - J - L
  • I = 18 - J - K

Note: I'm using letters (A, B, ..., L) instead of X1X2, ..., X12 because it's easier to write it like this here and because I don't know if the Xn notation is allowed on Maple (i don't think so).

So, the system is possible but undetermined (with 5 degrees of freedom), being F, H, J, K and L the free variables.

Until here, everything's fine. The problem arises when the professor asks us for every solution of the system that satisfies the condition that all the variables (form A to L) are positive integers (A, B, C, D, E, F, G, H, I, J, K, L ϵ IN → natural numbers).

From my understanding, that gives rise to a system of linear inequalities with 12 variables and the following inequalities:

  • A = 33 - K - L > 0
  • B = 1 + F - J > 0
  • C = -15 - F + J + K + L > 0
  • D = 15 + H - K > 0
  • E = 16 - F - H + J + K > 0
  • G = 34 - H - J - L > 0
  • I = 18 - J - K > 0
  • > 0
  • > 0
  • > 0
  • > 0
  • > 0                            (and A,B,C,D,E,F,G,H,I,J,K,L ϵ IN)



After some research, i found that a possible way to solve this type of system of linear inequalities is trough a method of elimination (analog to Gauss-Jordan's elimination method for systems of linear equations) named Fourier-Motzkin. But it's hardwork and i wanted to do it on the computer. After some research, i came across with the following Maple command:

SolveTools[Inequality][LinearMultivariateSystem]

http://www.maplesoft.com/support/help/Maple/view.aspx?path=SolveTools%2fInequality%2fLinearMultivariateSystem

So, I tried to use that command to solve my system, with the following result (or non-result):

with(SolveTools[Inequality]);
LinearMultivariateSystem({F > 0, H > 0, J > 0, K > 0, L > 0, 1+F-J > 0, 15+H-K > 0, 18-J-K > 0, 33-K-L > 0, 34-H-J-L > 0, -15-F+J+K+L > 0, 16-F-H+J+K > 0}, [F, H, J, K, L]);

Error, (in SolveTools:-Inequality:-Piecewise) piecewise takes at least 2 parameters


So, i really need help solving this as the professor told us that the first one to solve would win a book, eheh. I don't know what I'm doing wrong. Maybe this Maple command is not made for 12 variables? Or maybe i'm just writing something on a wrong form. I've never used Maple before so i can be doing something really stupid without knowing it.

I would really apreciate an answer, as my only goal as a future physicist is to unveil the secrets of the Cosmos to us all.

Thank you again.

Miguel Jesus





teliko.mwMapl_doc.docxHello,

After I have substitute all the variables by hand ,maple still continious  processing(27 hours and still evaluating)for a simple

summarisation by the time that live math2 needed only 2 mins.Have i done something wrong?I want to solve the following equation which is shown in the attached file with the experimental data

I actually had the same problem on Maple 16. When i go to plot an equation (usually on implicit plots) it just repeats the equation in blue text rather than showing any sort of plot. Im sure i am just missing a simple option somewhere, but for the life of me I cant find it. Any and all help would be appreciated. 

1 2 3 4 5 6 7 Last Page 1 of 19