i am using maple to solve a system of ordinary differential equations , 3 unknows (x,y, x ), and 3 equations (dx/dt,dy/dt,dz/dt)

there is one known variable denpendent on x and z

# code begins here

if x(t) <= z(t) then Q(t) := 8 end if;

if x(t) > z(t) then Q(t) := 10 end if;

eq1 := diff(x(t), t) = 3*x(t)-1;

eq2 := diff(y(t), t) = y(t)+Q(t);

eq3 := diff(z(t), t) = z(t);

eqs := {eq1, eq2, eq3};

# code ends here

above i put the system of ODEs, the code maybe illegal in maple, but i wrote in this way to make it clear.

Q is dependent on x and z.

in the past, when i was trying to solve ODEs, normally, eqs contains with only x,y,z as unknowns. but in this eqs, clearly, Q is included as an unknown. 

i've tried to use piecewise function to express Q(t), but failed.

how could i solve a system like this? thanks 

Hi,

how can I solve a set of first order, coupled, non-linear and inhomogeneous differential equations using MAPLE 12.

Hi, I have a bivariate generating function that looks like this

where x is enumerating by binary strings by length and k is counting a number patterns in the string. I would like to convert the series into partial fractions. Convert[parfrac] only seems to work when k is given a value, which I did for several small small choices, from which I guessed the general partial fraction decomposition. Would someone have an idea on how to extract the partial fractions directly in terms of x and k?

Thanks,

best, Luke

In the old version of Maple, the accurate value of Sin()and Cos() at some particular points, such as Pi/10, can be returned as below:

But in Maple 18, it just returns the same as the input.

How to make Maple18 return the accurate value as before?

i have a large angle and i wish to represent this angle called theta in the range [0 2*Pi]. In matlab this is done by the command mod(theta, 2* Pi). ihave tried frem and mod in maple but the two cannot accept 2*Pi as a second argument 

how can i do that 

Hello all!

I have to solve 1D Heat equation with Neumann B.C. using implicit scheme.

I have: 

I have my code in Maple for the solution of this problem using explicit sceme for Neumann B.C.. And I also have the solution of the problem using implicit scheme(but for Dirichle B.C.).

implicit_method_Dirichle_B.C..mws
explicit_method_Neumann_B.C..mws

I know that my Neumann B.C. for implicit scheme will be written like this.
I determined the ghost points and then got the final view of the B.Cs.:

But I can not imagine how I should put my Neumann  B.C. for implicit scheme in the code. 

Please, help me! I will be very grateful!

Here is the ODE:

dsolve((y(x)^2-x)*(D(y))(x)+x^2-y(x) = 0, {y(x)})

And the Maple 18 returns a very complex result.

But as we know,the more elegant result should be this:

How can I get this simple result with Maple?

Hello,

I would like to solve easily this equation with maple.

When i use solve or isolate functions, i have a result with arctan function.

"sol := solve(a*cos(gamma)+b*sin(gamma)+c, gamma):
isolate(a*cos(gamma)+b*sin(gamma)+c=0,gamma); "

It is good but i would like solutions with arccos.

In other words, i would like to have these calculations :

a*cos(gamma)+b*sin(gamma)+c=0

cos(psi)=a/sqrt(a²+b²)

sin(psi)=b/sqrt(a²+b²)

thus 

cos(psi)*cos(gamma)+sin(psi)*sin(gamma)=-c/sqrt(a²+b²)

cos(psi+gamma)=-c/sqrt(a²+b²)

gamma=-psi -/+ arccos(c/sqrt(a²+b²))

Is there a possibility to lead this calculation automatically with maple? For example, is it possible to force isolate function to seek for this kind of solution.

Thanks a lot for your help

Hello,

I often need to copy equations from maple with mathml option so as to copy it in my equations in mathtype in microsoft word.

Unfortunetaly, for a bit long equation, i often have troubles et i can't copy it in my mathtype equations.

Have you some ideas so as the copy in mathtype equations runs everytime ?

Thanks a lot for your help

I have a set of partial differential equations and want to find its conserved currents using PDE pakage. 

I define second order partial differential equations as q1,q2,q3,q4 and a set of them: PDE3:={q1,q2,q3,q4} and use the command J[alpha] := ConservedCurrents(PDE3) to calculate its conserved currents but I encounter this error which made me crazy!

Error, (in PDEtools:-DeterminingPDE) invalid input: PartialDerivatives expects value for keyword parameter maxdifforder to be of type nonnegint, but received -1

my equations are like

((1/2)*(diff(R(theta, psi), theta))*(diff(f(theta, psi), theta))+(3/8)*(diff(R(theta, psi), theta))^2+(1/8)*(diff(f(theta, psi), theta))^2+(1/4)*(diff(f(theta, psi), theta, theta))+(1/4)*(diff(R(theta, psi), theta, theta)))*exp(f(theta, psi))+diff(R(theta, psi), psi, psi)-(1/2)*(diff(R(theta, psi), psi))*(diff(f(theta, psi), psi))+(1/2)*(diff(chi(theta, psi), psi))^2 = 0

I don't know what's wrong, can you help me?

I have a differential equation system x'(t)=f1(k,t)*x(t)+f2(k,t)*y(t), x'(t)=g1(k,t)*x(t)+g2(k,t)*y(t) with initial condition x(0)=1 and y(0)=1. Here k is a parameter, f1, f2,g1, g2 are certain functions of k and t. I used dsolve and set k to be a parameter to solve the system numerically which gives you a procedure output. If I fixed k to be a specific numerical number, then I can use odeplot to plot x(t) VS t.

Now I set a range for k, say k=0..10. And I want to plot x VS (t,k) which is a 3D graph. How can I do this?

Hi MaplePrimers,

I've written a function that needs to be evaluated at a bunch of different points.  Evaluating it in a loop works. I'm wondering if there was a faster way to do this because I'm evaluating a list of 400k+ sets of points.  

Right now I'm using a loop with the following code.

for i from 1 to 500000 do 
     Results(i):= f(L[i][])[1];
od;

 

If I have a function f, which has 5 arguements, f(y, w, x,y,z).

I also have a list of those arguements:  L = [[1,2,3,2,3],[4,5,6,2,3],[7,8,9,2,3]]

What would be the fastest way to get a list of results?  Also, is there a way that I could preallocate memory for this list?

Ideally, I would like to get the output as as list.  ie:

Results:= [[f(1,2,3,2,3)], [f(4,5,6,2,3)], [f(7,8,9,2,3)]]

Hi all,

As we know that the differential of conjugate(z) is non-analytic.

But it seems that the diff gives the solution about the complex function conjugate(z)

What does it mean?

Hello guys, i have a system of equations ( dynamical system ) which i have its critical points but when i compute its critical points with maple i get different points , i dont know what is wrong . thank you for your time.

critical.mw

Is there any one to help me in calculating computational order of convergence of derivative free method. I am trying to calculate programs runs with immature error and does not print it.

Please is there any 1 to help.