I'm trying to solve a system of nonlinear differential equations. As a minimal working example, Maple is able to solve this just fine:

restart:

pde_sys :={diff(A(t1),t1)*cos(B(t1)) = 0, diff(A(t1),t1)*sin(B(t1)) = 0}:
solving_vars := {A(t1), B(t1)}:

dsolve(pde_sys, solving_vars);

This returns [{A(t1) = _C1}, {B(t1) = B(t1)}], as expected.

However, when simply adding an arbitrary dependence on a second variable, no solution is generated

restart:

pde_sys :={diff(A(t1,t2),t1)*cos(B(t1,t2)) = 0, diff(A(t1,t2),t1)*sin(B(t1,t2)) = 0}:
solving_vars := {A(t1,t2), B(t1,t2)}:

dsolve(pde_sys, solving_vars);

Of course, this has a solution: [{A(t1,t2) = _F1(t2)}, {B(t1) = B(t1,t2)}].

Using printlevel to debug, it seems the behavior diverges when dsolve attempts to call type/ODEtools/F(x). The univariate case correctly determines that A(t1) is of the type F(x); then, these functions are correctly passed to PDEtools/assign and execution continues nominally.

For the multivariate case, A(t1,t2) is not recognized as type F(x), so no functions are passed to PDEtools/assign and execution is dominated by null sets.

Is there something I'm missing here? Or is there another way to approach this problem?

Thanks!

How to linearize this equation by Taylor function?

or otherwise written:

sin(phi2)*sin(psi1(t))*lk*m1*(diff(psi1(t), t, t))+sin(phi2)*(diff(psi1(t), t))^2*cos(psi1(t))*lk*m1

Some one can help me?

Hi!

If i do something like this:

my_points := [[1, 2], [2, .9]];
plot(my_points, style = point)

It works ok. But then i try to take units in place:

my_scaled_points := [[1*Unit('kg'), 2*Unit('hour')], [21*Unit('kg'), 7*Unit('hour')]];
plot(my_scaled_points, style = point, useunits = [Unit('kg'), Unit('hour')])

..i got empty graph. How it can be fixed?

Thank you!

Is it possible to construct in Maple the following sequence of ascending fifths?:

3/2, 3^2/2^3, 3^3/2^4, 3^4/2^6, 3^5/2^7, 3^6/2^9, 3^7/2^11, 3^8/2^12 and so on. The result always more than 1 and less than 2.

Hello,

I'm quite new to Maple and as practise, I want to calculate some z-Transformations via the definition (sum).

sum(z^(-k),k=0..infinity) assuming abs(z)>1; this one works fine (after I added the convergence condition abs(z)>1.

sum(exp(a*k*Ta)*z^(-k),k=0..infinity) assuming abs(exp(a*Ta)*z^(-1))>1; doesn't work. But I if I change the convergence condition to a*Ta<ln(z), it is calculated correctly. Why does the first attempt not work? What is the correct way to tell maple the convergence condition?

Hi all

I would like to display 'Hello' or 'try again' to see the condition introduced is satisfied or not. 

if f(a) <0 then print( a, f(a));
display ('  Hello);
else
display( ' Tru again')

end if;

But this code does not work.

Thanks for any help.

Dear all

I solve an optimization problem ( minimization or maximization) using lagrangeMultiplier theorem 

The objective function is f:=(x,y,z) =x*y+y*z;

The constraints are: x*y=1  and y^2+z^2=1;

Using a numerical method I get the follwing point 

x = 1.41421356249703, y = .707106781124551, z = .707106781248575

How can I confirm that this point is a minumum or maximum

Maybe I must use Hessian matrix or something else.

Which condition must be introduced to know the type ( maximum or minumum) this point.

Many thanks for your help

I have a system of equation as

Hi all

I have a system of equation:

sys := [x+y, 2*x+y^2];

How can I convert the previous system to this function using maple

F:=(x,y)->(x+y,2*x^2+y^2);

then how can I compute the gradient of F.

Many thanks.

Hi there,

I have an ode that I want to plot, I am trying to plot 2 different graphs on one graph and have tried using display but cannot seem to add a legend to it. Someone suggested adding a legend to each individual graph before combining them but I cannot find out how to add a legend to a DEplot. My code is as follows:

ode:=diff(u(t),t$2)-0.1*(1-64*u(t)^2)*diff(u(t),t$1)+16*u(t)=0

Q1:=v/4*sin(4*t)+epsilon*(1/8*(v-v^3)*t*sin(4*t)+v^3/128*(cos(4*t)-cos(12*t)))

A:=DEplot(ode,u(t),t=0..10, [[u(0)=0, D(u)(0)=v]], u=-0.5..0.5, linecolor=black, linestyle=dash, title="Numerical Solution"):

B:=plot(Q1, t=0..10, u=-0.5..0.5,color=blue, legend="Regular Perturbation Expansion"):

display([A,B],title="Comparing the regular perturbation expansion to the numerical solution")

Many thanks

I would like to convert a symbolic expression to text commands.  I recently used the expression palette to create a series summation; however, I was confused whether the sigma represented Sum vs sum.  I attempted to convert to string, but MAPLE attempts to evaluate the symbolic series prior to outputting the text commands.  Unfortunately, the evaluation of the series is computationally expensive & MAPLE will run out of memory.  I do not need MAPLE to evaluate the series.  How can it simply spell out the text commands that represent the symbolic form without resorting to evaluating the expression?

Download convert_to_text_command.mw

I need to find the intersection points of two circles (x-7)^2+(y-2)^2=100 and (x-11)^2+(y-5)^2=75 using the modified Newton secant method. 

I have already done this by using these two equations to make one in terms of x. But, i am looking for suggestions on how to make a multiple variable version of the secant method.

Given a sequence for example: 8, 32,128,512,2048 and so on. Suppose we do not know it is 2^(2n +1). How to make Maple to find the principle?

Letter_Lrotate2D.mws

   I've asked a similar question before, and got the letters to rotate in 3D using the rotate command.  The resulting size in a 3D plot is relatively small..  The program gives a plotted letter L.  I wish to get some animation of it being rotated about the y-axis - but remaining in 2D.  ie looking at the letter it appears to be rotating.  To do thisI have multiplied the x-coords by the cosine of the angle of rotation.   

   In the for loop towards the end of the program there is a variable c1 which is incremented by one in the loop - yet it remains at 2, regardless of the angle increments.   Why is that?

  Again, any help or comments much appreciated.

Download test.mw
Udp: document attached.

Download test.mw

Hi!

I got a function (from CurveFitting), that produce a polynomial with the some units inside:

As i can see, it can be easy simplified, but i get:

Is where any trick to do it, without stripping units with convert(unit_free) or something?

Thank you!

Dear, I want to plot the graph for differerent values of F=10,20,30 one after the other  in the title automatic it should take the values of F and shown in the following sample here is my codes,  and sample graph

restart:
h:=z->1-(delta2/2)*(1 + cos(2*(Pi/L1)*(z - d1 - L1))):
K1:=((4/h(z)^4)-(sin(alpha)/F)-h(z)^2+Nb*h(z)^4):
lambda:=Int(K1,z=0..1):
L1:=0.2:
d1:=0.2:
alpha:=Pi/6:
plot( [seq(eval(lambda, Nb=j), j in [0.1,0.2,0.3])], delta2=0.02..0.1);