Hello,

I'm writing to ask how to equalize the coefficients of two multivariate polynomials. In particluar, I have two polynomials whose arguments are ln(E),ln(K),ln(L) (their levels, squared levels and interaction terms). The first one is:

(1/2*(p*a*b+(g-p)*b-g))*b*v*a*ln(E)^2-(-1+b)*v*(g-p+a*p)*b*a*ln(E)*ln(K)-b*p*(a-1)*v*a*ln(E)*ln(L)+v*a*b*ln(E)+(1/2*(p*(-1+b)*a+(g-p)*b+p))*(-1+b)*v*a*ln(K)^2+(-1+b)*v*p*(a-1)*a*ln(K)*ln(L)-v*a*(-1+b)*ln(K)+(1/2)*a*p*v*(a-1)*ln(L)^2-v*(a-1)*ln(L)

the second one is:

x_1*ln(E)+x_11*ln(E)^2+x_12*ln(E)*ln(K)+x_13*ln(E)*ln(L)+x_2*ln(K)+x_22*ln(K)^2+x_23*ln(K)*ln(L)+x_3*ln(L)`+x_33*ln(L)^2

I would like to know if it is possible to equalize the coefficients of the two polynomials and find the following system:

v*a*b = x_1, -v*(a-1) x_3, -v*a*(-1+b) = x_2, a*b*v*(b*rho*a-b*rho+g*(-1+b)) = x_11, v*rho*a*(a-1) = x_33, v*a*(rho*(-1+b)*a-rho*(-1+b)+b*g)*(-1+b) = x_22, -a*v*rho*(a-1)*b = x_13, -a*v*(a*rho-rho*u+g)*b*(-1+b) = x_12, a*v*u*rho*(a-1)*(-1+b) = x_23

I tried using "coeffs" and creating a sequence of values for x but then I don't know how to equalize them.

Thank you very much in advance for your time,

Elena

Hi everyone.

I'm trying to solve the following PDE

but I'm getting this error:

Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions can only contain derivatives which are normal to the boundary, got (D[1, 1](w))(x, 0)

The PDE represents the bending of a thin plate.

See File:

PDE-Problem.mw

into the "Ask a Question" window?

Nothing to add

Actually I want to ask something else.

(Maple 2015)

For the simple ODE with initial condition
dsolve({ diff(y(t),t) = y(t)^2 - y(t)^3, y(0) = 1/10 }, y(t));

dsolve produces two different answers, almost randomly (even after restart or after closing Maple and reloading the worksheet). Namely:

(1)

(2)

or

(2')

but this simplifies to (2), so it's not a "true" bug.

Notice that (2) is correct but (1) is incorrect even for t=0 (the initial condition!):

evalf(eval(RootOf(-ln(_Z)*_Z+ln(_Z-1)*_Z-ln(10)*_Z-ln(9/10)*_Z-I*Pi*_Z+_Z*t-10*_Z+1),t=0))=1/10;

Maple seems to prefer the wrong solution (1) but occasionally produces (2) e.g. in a new whorksheet!
In earlier versions it seems that only (1)  appears.

The same ODE with another IC

dsolve({ diff(y(t),t) = y(t)^2 - y(t)^3, y(0) = 1/100 }, y(t));

evalf(eval(%,t=0));

is always incorrect. It should be

but Lambert's function never shows up!
Let me mention that only the exact solutions are affected, numeric is ok.

Without an initial condition, dsolve always uses LambertW:

dsolve({ diff(y(t),t) = y(t)^2 - y(t)^3}, y(t));

Can you explain this behavior?

Dear Friends

My problem is related to exporting Maple code to Latex, to be more specific I want Latex output that look exactly same as it appears in Maple worksheet like like Red Maple prompt etc.

I have found another solution to this:

"In file menu go to “Export As”, then save file in Tex format. But in order to run this Tex file you need to have files like maple2e.sty, mapleenv.sty, maplestd2e.sty, mapletab.sty, mapleenv.def, mapleplots.sty, maplestyle.sty, mapleutil.sty(all part of package maplestd2e), these all file can be copied from C:drive where maple is installed, just copy all these file to Latex folder and you can run Tex file exported from Maple."

But this do not give exactly what I want.

Please see Maple file and its exported Tex version(Not possible to upload) along with pdf output for Maple worksheet.

Maple_Export_to_Latex.pdfMy_Paper_on_Zakharov-Kuznetsove_equation_(Simplified_determining_equations_for_classical_symmetries).mw

Let A and B be two lists of monomials. I want a new list C contained that monomials of A where not divide by any monomial of B. For example if A=[x,y,x^2y,xy^2,y^2] and B=[x^2,y^3] then C=[x,y,xy^2,y^2].

I am getting the following expression when I partially differentiate an expression:

PDE11 := diff(theta(z, p), z, z, p)+2*lambda(p)*theta(z, p)*(diff(lambda(p), p))+lambda(p)^2*(diff(theta(z, p), p))+lambda(p)^2*(sin(theta(z, p))-theta(z, p))+2*p*lambda(p)*(sin(theta(z, p))-theta(z, p))*(diff(lambda(p), p))+p*lambda(p)^2*(cos(theta(z, p))*(diff(theta(z, p), p))-(diff(theta(z, p), p)))

I differentiate the above equation to get each term in the form of :table([f=......])

(table([f = 1+sum(Lambda[n](0)/factorial(n), n = 1 .. infinity)]))(p)^2

It is difficult to understand the expression. Maple does not show any error. Can you please tell me what the error is?

Hi, I am trying to find adomian's polynomial of exp(y), but after execution it shows DF(e^y), D^2F(e^y) as it is. why it does'nt show its derivative?plz help meNewADP.2.mw

Hi, I am working on an assignment and I am having difficulties with this Eurler method since I am working with vector.

The assignment:

If the aircraft's engine transmits power P to the air, the force of the propellar, Fp, satisfies P=Fpv. Since the force Fp acts in the direction of motion, it can be written in vector form as: (what I have so far)

with(linalg);

v:=Vector(2,1,[vx,vy]); velocity vector

nu:=v->Norm(Vector(v),2); (length of v)

Fd:=-1/2*C*rho*A*nu*v # air resistance

Fl:=1/2*Cl*rho*A*nu*v # liftforce in y direction here v=[-vy,vx]

Fp:=(P/nu^2)*v^2 # power from aircraft

All this adds up to:

F_T:=v->Vector(evalm(Fp/nu(v)^2*v+Fd*nu(v)*v+Fl*nu(v)*zip((x,y)->x*y,v([2,1]),Vector([-1,1]))+Vector(2,1,[0,-m*g]))); # I have tried it and it works

so up til here I am good. It is this next part that I can't seam to get.

Write a routine which uses Euler's method to solve the equation of motion numerically for velocity v(t):

m*dv/dt=F_T(v)

Test the program by trying a plane with intitial velocity [v0,0] such that it maintains this speed when the engines power is P=P0

We have been given an Esolve we can use:

Esolve:=proc(f::procedure,h,x0,y0,N::integer) # Calculates y(x0+n*h) for n=1..N given y0=y(x0) and f(x,y)

local n,y,x;

y[0]:=y0; # Start Value
x:=x0;

for n from 1 to N do
y[n]:= y[n-1]+h*f(y[n-1],x); # Euler's formula
x:=x+h; # Next x
end do;

y;

end proc;

If anyone could help me understand how it works and how to get this to work with vectors I would be very gratefull.

Vahid Borji

How can I plot the p stability region in H₁and H₂ region I already gotten the polynomial 

Hi every body.

I want to solve a differential equation:

ode=D(r(θ),θ).....

I have the initial conditions:

e=10^(-20)

r(e)=A where A is parameter.
r'(e)=0

sol:=dsolve({ode,r(e)=A,D(r)(e)=0},parameter=[A],numeric)

and:

All in the file.

#@#

Ode-Problem.mw

hi every one

please see attached file blew and help me for dsolve set equations.i dont know aboue errors with in

thanks

equation.mw

When solving ODE with dsolve, I don't want to use "_C1" as the name of constant, I want to specify by myself, how can I do?

Take for instance the signal [1,0,-3,2,1,0,1,2] (considered in Wavelets for Kids, Vidakivic & Mueler, AMS, 1991).

I want to anlalyse it down to the level zero with Haar wavelets. It seems that MAPLE's commnad only applies once.