MaplePrimes Questions

I have some trouble solving the pde of:
ut + u^2*ux = u, u(x,0) = x, with x::real and t>0.

I think that I have 2 problems.

1.
The first part of the code I define u(x,t) with both the variable rp.
Then I define the variable q copying the definition of u(x,t).
When I try to insert q and u(x,t) in the initial equation - one is able to be reduced to one term while the other isn't.
So I'm not really sure what is happening here.

2.
When I use Maple's pdsolve() I get a result, but when I insert the answer in the initial equation - then it isn't correct.
I tried to show this in the last part of the code.

 

 

 

# ut + u^2*ux = u, u(x,0) = x

restart

rp := (-1 + sqrt(1 + 4*exp(t)^2*t*x))/(2*exp(t)^2*t);

(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/((exp(t))^2*t)

(1)

u := (x,t) -> rp*exp(t):
'u(x,t)' = u(x,t);

u(x, t) = (1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t)

(2)

q := (-1 + sqrt(1 + 4*exp(t)^2*t*x))/(2*exp(t)*t); # Copying the result from above and defining q the same

(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t)

(3)

# Now doing the same operations on supposedly the same term, but one is able to be reduced with assumptions while the other isn't.

L_nothing := diff(u(x,t),t) + u(x,t)^2*diff(u(x,t),x) ;
L_real := diff(u(x,t),t) + u(x,t)^2*diff(u(x,t),x) assuming x::real;
L_t := diff(u(x,t),t) + u(x,t)^2*diff(u(x,t),x) assuming t>0;
L_all := diff(u(x,t),t) + u(x,t)^2*diff(u(x,t),x) assuming t>0, x::real;

(1/4)*(8*(exp(t))^2*t*x+4*(exp(t))^2*x)/((1+4*(exp(t))^2*t*x)^(1/2)*exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t^2)+(1/4)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))^2/(exp(t)*t^2*(1+4*(exp(t))^2*t*x)^(1/2))

 

(1/4)*(8*(exp(t))^2*t*x+4*(exp(t))^2*x)/((1+4*(exp(t))^2*t*x)^(1/2)*exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t^2)

 

(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t)+(1/4)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))^2/(exp(t)*t^2*(1+4*(exp(t))^2*t*x)^(1/2))

 

(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t)

(4)

L_nothing := diff(q,t) + q^2*diff(q,x) ;
L_real := diff(q,t) + q^2*diff(q,x) assuming x::real;
L_t := diff(q,t) + q^2*diff(q,x) assuming t>0;
L_all := diff(q,t) + q^2*diff(q,x) assuming t>0, x::real;

(1/4)*(8*(exp(t))^2*t*x+4*(exp(t))^2*x)/((1+4*(exp(t))^2*t*x)^(1/2)*exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t^2)+(1/4)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))^2/(exp(t)*t^2*(1+4*(exp(t))^2*t*x)^(1/2))

 

(1/4)*(8*(exp(t))^2*t*x+4*(exp(t))^2*x)/((1+4*(exp(t))^2*t*x)^(1/2)*exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t^2)+(1/4)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))^2/(exp(t)*t^2*(1+4*(exp(t))^2*t*x)^(1/2))

 

(1/4)*(8*(exp(t))^2*t*x+4*(exp(t))^2*x)/((1+4*(exp(t))^2*t*x)^(1/2)*exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t^2)+(1/4)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))^2/(exp(t)*t^2*(1+4*(exp(t))^2*t*x)^(1/2))

 

(1/4)*(8*(exp(t))^2*t*x+4*(exp(t))^2*x)/((1+4*(exp(t))^2*t*x)^(1/2)*exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t)-(1/2)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))/(exp(t)*t^2)+(1/4)*(-1+(1+4*(exp(t))^2*t*x)^(1/2))^2/(exp(t)*t^2*(1+4*(exp(t))^2*t*x)^(1/2))

(5)

restart

pde := diff(u(x,t),t) + u(x,t)^2*diff(u(x,t),x) = u(x,t);
ic := u(x,0) = x;

diff(u(x, t), t)+u(x, t)^2*(diff(u(x, t), x)) = u(x, t)

 

u(x, 0) = x

(6)

pdsolve([pde, ic]);

u(x, t) = exp(t)*((2*exp(2*t)*x-2*x+1)^(1/2)-1)/(exp(2*t)-1)

(7)

u := (x,t) -> exp(t)*(sqrt(2*exp(2*t)*x - 2*x + 1) - 1)/(exp(2*t) - 1);

proc (x, t) options operator, arrow; exp(t)*(sqrt(2*exp(2*t)*x-2*x+1)-1)/(exp(2*t)-1) end proc

(8)

L := diff(u(x,t),t) + u(x,t)^2*diff(u(x,t),x) assuming t>0, x::real;

exp(t)*((2*exp(2*t)*x-2*x+1)^(1/2)-1)/(exp(2*t)-1)+2*exp(t)*exp(2*t)*x/((2*exp(2*t)*x-2*x+1)^(1/2)*(exp(2*t)-1))-2*exp(t)*((2*exp(2*t)*x-2*x+1)^(1/2)-1)*exp(2*t)/(exp(2*t)-1)^2+(1/2)*(exp(t))^3*((2*exp(2*t)*x-2*x+1)^(1/2)-1)^2*(2*exp(2*t)-2)/((exp(2*t)-1)^3*(2*exp(2*t)*x-2*x+1)^(1/2))

(9)

LL := simplify(L) = u(x,t)

exp(t)*(2*exp(2*t)*x-(2*exp(2*t)*x-2*x+1)^(1/2)-2*x+1)/((2*exp(2*t)*x-2*x+1)^(1/2)*(exp(2*t)-1)) = exp(t)*((2*exp(2*t)*x-2*x+1)^(1/2)-1)/(exp(2*t)-1)

(10)

evalb(LL)

false

(11)

# Obviously not correct solution... or what?

``

 

 

Download asol1-1.mw

 

 

I just  found what seems to be a serious problem and I am not able to figure if it is related to my own installation or not.

After I installed Physics 426 (Published on Sept 17, 2019) using the Maple GUI install button (which now works for my PC), I found I am not able to integrate basic things.

It seems to affect int when using some build in function with definite integration, but it could be others also. I need to test more. 

Could someone see if they get same problem as well?  

Could also someone please remind me of the library  commands to issue in order to remove current Physics version 426 and install earlier Physics version package, say 425, or any other version, so that  to see if this is related to version of a physics package or not?

restart;

version()

 User Interface: 1399874
         Kernel: 1399874
        Library: 1399874

1399874

interface(version)

`Standard Worksheet Interface, Maple 2019.1, Windows 10, May 21 2019 Build ID 1399874`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 426 and is the same as the version installed in this computer, created 2019, September 20, 23:28 hours, found in the directory C:\Users\me\maple\toolbox\2019\Physics Updates\lib\`

infolevel[int] := 3:

int(exp(x),x=0..1)

Definite Integration:   Integrating expression on x=0..1

Definite Integration:   Using the integrators [distribution, piecewise, series, o, polynomial, ln, lookup, cook, ratpoly, elliptic, elliptictrig, meijergspecial, improper, asymptotic, ftoc, ftocms, meijerg, contour]
LookUp Integrator:   unable to find the specified integral in the table
int/elliptic: trying elliptic integration
Integration Warning:   Integration method ftoc encountered an error in IntegrationTools:-Definite:-Main:
 mismatched multiple assignment of 2 variables on the left side and 1 value on the right side

Definite Integration:   Returning integral unevaluated.

int(exp(x), x = 0 .. 1)

restart;

int(sin(n*x),x=0..Pi)

int(sin(n*x), x = 0 .. Pi)

int(tan(x),x=0..Pi)

int(tan(x), x = 0 .. Pi)

int(cos(x),x=0..1)

int(cos(x), x = 0 .. 1)

int(sin(x),x=0 .. Pi)

int(sin(x), x = 0 .. Pi)

int(cos(x),x)

sin(x)

int(x,x=0 .. 1)

1/2

 

Download int_not_working.mw

@Torre 

with(DifferentialGeometry);
with(Tensor);
with(LieAlgebras);
DGsetup([x, y], M);
g1 := evalDG(dx &t dx);
Christoffel(g1);
Error, (in DifferentialGeometry:-Tensor:-Christoffel) expected 1st argument to be a metric tensor. Received: _DG([["tensor", M, [["cov_bas", "cov_bas"], []]], [`...`]])

 

I still get an error.  I was able to succeed in another example (when I copied the whole maple example.

Somehow, I cannot get the correct syntax.

Any help would be welcome.  The only explanation is that somehow the definition of the neutral tensor operator is missing.

Why Maple 2019.1 gives an error when no initial conditions are given for the following heat PDE with periodic BC?

I am using Physics 426 (current version). On windows 10.

When adding ic as some arbitrary function f(x), then the error goes away. But no ic needs to be given to solve this PDE. The answer can be left using arbitrary constants in this case.

I also found that this seems to happen when the BC are periodic. When using the normal Dirichlet B.C. and omitting the initial conditions, the error went away.

Am I doing something wrong or is this a bug?

restart;

pde:=diff(u(x,t),t)=diff(u(x,t),x$2); #try with NO IC
bc:=u(-Pi,t)=u(Pi,t),D[1](u)(-Pi,t)=D[1](u)(Pi,t);
pdsolve([pde,bc],u(x,t))

diff(u(x, t), t) = diff(diff(u(x, t), x), x)

u(-Pi, t) = u(Pi, t), (D[1](u))(-Pi, t) = (D[1](u))(Pi, t)

Error, (in pdsolve/BC/2nd_order/Series/TwoBC) invalid boolean expression: NULL

restart;

pde:=diff(u(x,t),t)=diff(u(x,t),x$2)-u(x,t); #now try with IC
bc:=u(-Pi,t)=u(Pi,t),D[1](u)(-Pi,t)=D[1](u)(Pi,t);
ic:=u(x,0)=f(x);
pdsolve([pde,bc,ic],u(x,t)); #solution is correct

 

diff(u(x, t), t) = diff(diff(u(x, t), x), x)-u(x, t)

u(-Pi, t) = u(Pi, t), (D[1](u))(-Pi, t) = (D[1](u))(Pi, t)

u(x, 0) = f(x)

u(x, t) = exp(-t)*_C7[0]+Sum(exp(-t*(n^2+1))*(sin(n*x)*_C1[n]+cos(n*x)*_C7[n]), n = 1 .. infinity)

restart;

pde:=diff(u(x,t),t)=diff(u(x,t),x$2); #now try with NO IC, but not periodic BC
bc:=u(0,t)=1,u(Pi,t)=0;
pdsolve([pde,bc],u(x,t)); #solution is correct

diff(u(x, t), t) = diff(diff(u(x, t), x), x)

u(0, t) = 1, u(Pi, t) = 0

u(x, t) = ((Sum(sin(n*x)*exp(-n^2*t)*_C1(n), n = 1 .. infinity))*Pi+Pi-x)/Pi

 

 

Download problem_09_20_2019.mw

I'm pretty annoyed with maple because when I try to create proc's it dooes not use tabbing or smart tabbing. This makes writing readable code a chore. Basically it's always screwing up alignment. (it wants to left justify things a lot)...

 

What's worse is that using the tab key takes one outside the proc rather than adding a tab, making one having to use spaces.

Any way to fix this?

I have an equation to solve 

mu*f = (2*S1*f + S1*x)

where mu is scalar, f is vector, x is vector, S1 is a matrix. I need to solve this equation for f but S1 is matrix sow can I tell Maple that S1 is matrix? If we solve the equation with matrix we need to use matrices inverse. If we have to divide by matrix we use the product of the inverse of this matrix.

For example, if I have a function

f:=x->x^3-2x

I want to created csv file containing coordinates of points of the function

(1,...), (1.1,...),...

 

How to do it?

 

I want to convert the coordinates to csv file and use this file in originpro to plot a graph that is more beautiful than that of Maple.

Hi,

I have this code to calculate taylor method but I do not know how to write the part about derivative of a function f  inside the loop for ??

restart;
f:=(t,y)->y-t^2+1:
eqn:=diff(y(t),t)=y(t)-t^2+1:
ex:=dsolve({eqn,y(0)=0.5},y(t)):
t[0]:=0:w[0]:=0.5:h:=0.2:ex[0]:=0.5:e[0]:=0:
for n from 1 to 10 do
t[n]:=n*h;ex[n]:=t[n]^2 + 2*t[n] + 1 - exp(t[n])/2;
w[n]:=w[n-1]+h*f(t[n-1],w[n-1])+((h^2/factorial(2))*(f(t[n-1],w[n-1])-2*t[n-1]));
e[n]:=abs(ex[n]-w[n]);
od:

printf(" i | t[i] |(Taylor)w[i] |(exact)y[i] |Error | \n ");for i from 0 to n-1 do
printf("%2.2f| %5.2f  | %5.6f| %5.6f  |  %5.6f | \n", i, t[i], w[i] ,ex[i],e[i]) ;
od;

Hi i was trying to numerically integrate my freinds model with dsolve, and i am sure that I have put all the right components in the command as described in the help page, but it doesn't work. (Here is a worksheet with the model Lindas_signal_transduction_model.mw )

What is the problem with the way I have called the function?
Does anyone have a mental checklist that they use for dsolve commands? because I often struggle with making them work.

 

Can you help me

myproc := proc () local img1, img2, img3;

with(DocumentTools); with(DocumentTools:-Layout);

img1 := "c:\\1.jpg"; img2 := "c:\\2.jpg"; img3 := "c:\\3.jpg";

print("Title 1 row 1, picture 1"); print(img1); print("Title 2 row 2, picture 2");

print(img2); print("Title 3 row 3, picture 3"); print(img3);

print("The End");

end proc

``

myproc := proc () local img1, img2, img3; with(DocumentTools); with(DocumentTools:-Layout); img1 := "c:\\1.jpg"; img2 := "c:\\2.jpg"; img3 := "c:\\3.jpg"; print("Title 1 row 1, picture 1"); print(img1); print("Title 2 row 2, picture 2"); print(img2); print("Title 3 row 3, picture 3"); print(img3); print("The End") end proc:

``


 

Download insert_picture.mw

print monitor

 

 

Hello all
I'm working on calculating the conservation laws for a Gardner equation
During calculation interface problem using []

The problem is that this function only works for integer exponents

Is there another way to overcome this

 


 

``

restart; with(PDEtools); declare(u(t, x), A(t), B(t), F(t))

` u`(t, x)*`will now be displayed as`*u

 

` A`(t)*`will now be displayed as`*A

 

` B`(t)*`will now be displayed as`*B

 

` F`(t)*`will now be displayed as`*F

(1)

det_eqs := [2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx)) = 0, 2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx)) = 0, 2*(diff(Lambda1(t, x, u, ux, uxx), uxx))*B(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*B(t)*uxx+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*F(t)*u+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n*ux = 0, 2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*ux+2*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*uxx-2*(diff(Lambda1(t, x, u, ux, uxx), ux))+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x)) = 0, 3*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*B(t)+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*B(t)*uxx+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*A(t)*u^n*ux = 0, ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))-ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))+uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))+2*uxx*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))+diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x) = 0, 2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*A(t)*u^n*ux+4*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*B(t)+4*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*B(t)*uxx+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*B(t)*uxx^2+4*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*B(t)+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*F(t)+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*B(t)*uxx+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*F(t)*u+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n*n*ux^2/u+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*A(t)*u^n*ux^2+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*B(t)*uxx+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*A(t)*u^n*ux = 0, 2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*B(t)*uxx+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*A(t)*u^n*ux^3+ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*B(t)*uxx+ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*A(t)*u^n*ux^2-(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*A(t)*u^n*ux^2-ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*F(t)*u-2*uxx*(diff(Lambda1(t, x, u, ux, uxx), ux))*A(t)*u^n-(diff(Lambda1(t, x, u, ux, uxx), x))*A(t)*u^n+uxx*(diff(Lambda1(t, x, u, ux, uxx), uxx))*F(t)+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*F(t)*u+2*ux^2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*F(t)+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*B(t)*uxx^2+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), x))*B(t)+ux^2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), u))*B(t)+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*F(t)+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*B(t)*uxx^3-ux*(diff(Lambda1(t, x, u, ux, uxx), ux))*F(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*B(t)*uxx^2-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))*F(t)*u+uxx*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*B(t)+2*uxx*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*F(t)+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*A(t)*u^n+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*F(t)*u+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*A(t)*u^n*n*ux^2/u+3*uxx*(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n*ux/u+3*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*A(t)*u^n*ux+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*A(t)*u^n*ux+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*A(t)*u^n*ux-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))*A(t)*u^n*ux+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*A(t)*u^n*ux^2+2*uxx*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*F(t)*u-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*F(t)*u-(diff(Lambda1(t, x, u, ux, uxx), t))+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*B(t)*uxx^2+2*uxx^2*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*A(t)*u^n+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*F(t)*u+2*(diff(Lambda1(t, x, u, ux, uxx), u))*B(t)*uxx+(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*B(t)*uxx+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*B(t)*uxx+(diff(Lambda1(t, x, u, ux, uxx), u))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*A(t)*u^n*ux-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*A(t)*u^n*ux+Lambda1(t, x, u, ux, uxx)*F(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), x), x))*B(t)+uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*F(t)*u+2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*A(t)*u^n*n*ux^3/u+(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n^2*ux^3/u^2-(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n*ux^3/u^2+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*A(t)*u^n*n*ux^2/u-(diff(Lambda1(t, x, u, ux, uxx), ux))*A(t)*u^n*n*ux^2/u = 0, diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx) = 0, diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx) = 0]

[2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx)) = 0, 2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx)) = 0, 2*(diff(Lambda1(t, x, u, ux, uxx), uxx))*B(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*B(t)*uxx+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*F(t)*u+(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n*ux = 0, 2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*ux+2*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*uxx-2*(diff(Lambda1(t, x, u, ux, uxx), ux))+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x)) = 0, 3*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*B(t)+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*B(t)*uxx+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx))*A(t)*u^n*ux = 0, ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))-ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))+uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))+2*uxx*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))+diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x) = 0, 2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*A(t)*u^n*ux+4*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*B(t)+4*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*B(t)*uxx+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*B(t)*uxx^2+4*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*B(t)+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*F(t)+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*B(t)*uxx+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*F(t)*u+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n*n*ux^2/u+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx))*A(t)*u^n+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*A(t)*u^n*ux^2+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*B(t)*uxx+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), x))*A(t)*u^n*ux = 0, (diff(Lambda1(t, x, u, ux, uxx), u))*F(t)*u-ux*(diff(Lambda1(t, x, u, ux, uxx), ux))*F(t)+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*A(t)*u^n*ux-(diff(Lambda1(t, x, u, ux, uxx), x))*A(t)*u^n+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), x))*B(t)+ux^2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), u))*B(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*B(t)*uxx^2+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*F(t)*u+2*(diff(Lambda1(t, x, u, ux, uxx), u))*B(t)*uxx-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*F(t)*u+2*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*F(t)+uxx*(diff(Lambda1(t, x, u, ux, uxx), uxx))*F(t)+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*A(t)*u^n*n*ux^2/u+3*uxx*(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n*ux/u-(diff(Lambda1(t, x, u, ux, uxx), t))+2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*A(t)*u^n*n*ux^3/u+(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n^2*ux^3/u^2-(diff(Lambda1(t, x, u, ux, uxx), uxx))*A(t)*u^n*n*ux^3/u^2+2*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*A(t)*u^n*n*ux^2/u-(diff(Lambda1(t, x, u, ux, uxx), ux))*A(t)*u^n*n*ux^2/u+2*uxx^2*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*A(t)*u^n+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*F(t)*u+uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*F(t)*u+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*B(t)*uxx^2+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x), x))*B(t)*uxx+(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*B(t)*uxx+uxx*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*B(t)+2*uxx*ux*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx))*F(t)+2*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), x))*A(t)*u^n+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*B(t)*uxx^3+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*B(t)*uxx^2+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*A(t)*u^n*ux^2+2*uxx*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux), uxx))*F(t)*u+3*uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*A(t)*u^n*ux+2*uxx*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), uxx), x))*A(t)*u^n*ux+uxx^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux), uxx))*A(t)*u^n*ux-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))*A(t)*u^n*ux+2*ux^2*(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx))*F(t)-uxx*(diff(diff(Lambda1(t, x, u, ux, uxx), ux), ux))*F(t)*u-ux*(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*F(t)*u-2*uxx*(diff(Lambda1(t, x, u, ux, uxx), ux))*A(t)*u^n+ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*F(t)*u+2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*A(t)*u^n*ux^2-(diff(diff(Lambda1(t, x, u, ux, uxx), u), ux))*A(t)*u^n*ux^2+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*B(t)*uxx+2*ux*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), uxx), x))*F(t)*u+(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*A(t)*u^n*ux^3+ux^2*(diff(diff(diff(Lambda1(t, x, u, ux, uxx), u), u), uxx))*B(t)*uxx-(diff(diff(Lambda1(t, x, u, ux, uxx), ux), x))*A(t)*u^n*ux+Lambda1(t, x, u, ux, uxx)*F(t)+(diff(diff(Lambda1(t, x, u, ux, uxx), x), x))*B(t) = 0, diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx) = 0, diff(diff(diff(Lambda1(t, x, u, ux, uxx), uxx), uxx), uxx) = 0]

(2)

CL_multipliers := [Lambda1(t, x, u, ux, uxx)]

[Lambda1(t, x, u, ux, uxx)]

(3)

simplified_eqs := DEtools[rifsimp](det_eqs, CL_multipliers, mindim = 1)

Error, (in DEtools/Rif/setup) simplification for integer exponents

 

``

``

``

 

 
 

Download question_for_rif

 

Hello

I found this example in the Help.

I'm wanting to export the encrypted file (the gibberish between local and end proc) to friend running another M2018, and want it to run.

I would need to rerieve "abc.mla" repository that we saved it in. But I cant find it. and if i did send it, he would be able to decrypt it surely?

Encrypt_Proc.mw

 

Hi,
I had written some help pages in Maple 18 that I just migrate in Maple 2018.
This seems correct except one single point: when I try ot access them from the help menu, their names are preceeded by a  "WS" label and, when I click on it, the help page appears in a new window of my Maple's session, not in the help window.
I guess "WS" means "WorkSheet" ?
How can I force the halp page of "my" function to appear in the main help page window?

(hope I was clear enough)

Thanks in advance
 

 

 

I want to calculate the voltage between phase 1 and phase N in an electrical circuit:

 

The vectorial formula is:

`#mover(mi("U"),mo("→"))`[L1-N]-`#mover(mi("ΔU",mathcolor = "blue"),mo("→",mathcolor = "blue"))`[L1]+`#mover(mi("ΔU",mathcolor = "#339966"),mo("→",mathcolor = "#339966"))`[N] = `#mover(mi("U",mathcolor = "red"),mo("→",mathcolor = "red"))`[L1-N]

 

Voltage drops are calculated with the current multiplied with the resistance: ΔU = I*Z[L]

 

i

 

-`#mover(mi("I",mathcolor = "blue"),mo("→",mathcolor = "blue"))`[L1]*`#mover(mi("Z",mathcolor = "#ff99cc"),mo("→",mathcolor = "#ff99cc"))`[L]+`#mover(mi("I",mathcolor = "#339966"),mo("→",mathcolor = "#339966"))`[N]*`#mover(mi("Z",mathcolor = "#ff99cc"),mo("→",mathcolor = "#ff99cc"))`[L]+`#mover(mi("U"),mo("→"))`[L1-N] = `#mover(mi("U",mathcolor = "red"),mo("→",mathcolor = "red"))`[L1-N]NULL

This is a real example with realistic values and angles. Note that i have two different vectors with the same index.

This is on purpose and the vector is different. This is because the first vector is before the resistance in the wire and

the one i want to find, is after the resistance in the wire (the red one).:

``

"(U[L1-N])=230∠0°"

"(I[L1])=20∠-30°"

"(Z[L])=0.097∠7.2°"

"(I[N])=40∠-120°"

 

The negative angles is because i am using my reference which is in 0°. And are the vector to the right of my reference is the angle negative, and is it on the left of my reference is the angle negative. I dont want to explain the vectorial diagram, because i think it will do more confusion than explaining.

 

``

"230∠0°-(20∠-30°*0.097∠7.2°)+(40∠-120°*0.097∠7.2°)=(U[L1-N])"

 

My question is, if the formula above is possible to solve in maple?

 

 

The result is calculated on my CAS-calulator:

 

"(U[L1-N])=226 V∠-0.7°"``

``


The example in Maple:

Download Example_to_Mapleprimes.mw

 

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