## Plotting a following PDE...

restart;
PDE := diff(y(x,t), x,x,x,x)+(diff(y(x, t), t,t))=0;
# Initial/boundary conditions
BCs:=y(0,t) = 0, y(1,t) = 0,D[1](y)(0,t)=0,D[1](y)(1,t)=0;

ICs:=y(x,0) =0, D[2](y)(x,0)=1 ;
num_solution := pdsolve(PDE, {BCs,ICs}, numeric);
num_solution :-plot3d(x=0..1, t=0..1);


1st Question:How to plot the 2D at point x=0.5?

2nd Question: How to use PDEplot?

## Stability of a system...

How to use a Lyapunov function to prove the stability of a system of differential equations and then check the stability? My initial thoughts were to use a contour plot?

I havev to calculate the intersection of three planes and need to plot them, when I try to plot them I get this error:

Error, (in plot3d) bad range arguments: (Vector(3, {(1) = -4*_t2[3], (2) = 3*_t2[3], (3) = _t2[3]})) = -8 .. 8, y = -20 .. 20

This is my code so far:

with(LinearAlgebra);
A := <1, 1, -2|3, 4, -7|-5, -8, 13>
b := <0,0,0>

x := LinearSolve(A, b)
P1 := x+3*y;
P2 := x+4*y;
P3 := -2*x-7*y;
plot3d([P1, P2, P3], x = -8 .. 8, y = -20 .. 20, plotlist = true, color = [blue, red, green]);
Error, (in plot3d) bad range arguments: (Vector(3, {(1) = -4*_t2[3], (2) = 3*_t2[3], (3) = _t2[3]})) = -8 .. 8, y = -20 .. 20

## Book Suggestions for improving Maple...

Hello,

I will buy some books for improving Maple.

Especially, I'm looking for the good books with Maple code for solving differential equations (Analytical and numerical solutions for Both Ordinary and Partial Differential equations).

Book Language: English.

Best regards.

## How to restrict a function to a "y" value?...

Hello,

I am currently doing this thing:

unapply(piecewise(x>37-0.25*t and x<37+0.25*t,-(11*sin(t/2+1.145)-10)*((x-37)^2)+(-3.5*sin(t)+ 1),10),x);

(It is used with "for t from 0 to 8 do *things* end do", hence why I use "t")

The problem I have is I don't want this (over) complicated function to go over y=10, but the conditions I tried were not working that well.

I saw on the Help page that it should be possible, but my attempts were unsuccessful...

## bug in Latex generation...

Maple 2018.2 generates wrong latex in this example. In Latex a space in command name is important. So "\tau L" is not the same as "\tauL".  Since in the later case, Latex will complain that there is no command "\tauL"

Maple generates "\tauL" in the latex, when it should be "\tau L" in the following example, so the latex fails to compile because there is no command called "\tauL" in Latex.

Here is screen shot showing the problem and the Maple command to reproduce it

restart;
interface(showassumed=0);
pde :=  diff(u(x,t),t)=k*diff(u(x,t),x\$2)+(exp(-c*t)*sin(2*Pi*x/L));
ic  :=  u(x,0)=f(x);
bc  :=  D[1](u)(0,t)=0, D[1](u)(L,t)=0;
sol:=pdsolve({pde,ic,bc},u(x,t)) assuming L>0,t>0,k>0;

latex(sol)

Any chance Maplesoft could fix this?

Possible workaround for now is to use something like "\newcommand{\tauL}{\tau L}" in preamble for this specific case.

How could this be set up in Maplesim?  A vibration signal is imparted on the box and we want to observe the behavior of the sprung object inside the box.

## Get the "union" of a list of "intervals"...

Hello,

Assume we have the following "intervals" (I am not sure what is its formal name in Maple)

C :=[0,1/11],[1/11,1/9],[1/9, 1/7],[1/3,1/2],[1/2,1]

How can we get the "union" of these intervals? That is to say, obtain  [0,1/7],[1/3,1]

## How do I plot 3d equations of motion in maple?...

Hi,

I'm trying to plot a 3 dimensional vector equation of motion in Maple for my dissertation. The equation is as follows:

vec(vr) = (vb)*i + (vg*cos(Omega*t))*j + (vg*sin(Omega*t))*k

where Omega is the gyrofrequency, vb is the velocity parallel with the i direction, and vg is the perpendicular velocity of gyration. vg and vb are both in terms of the velocity of incidence and two angles, which are all just numerical values that I've introduced.

It should look like a helix spiralling around the i axis, but I'm fairly new to Maple and I've tried everything I can think of and I can't get it to work.

When I use plot3d it turns out looking like a sphere or a cylinder. When I use spacecurve, it doesn't work at all and I get the error message " Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct.".

Any help is greatly appreciated.

## Multipliying the solution found by Runge Kutta me...

I have an ODE. I solved it numerically by Runge Kutta method.

The solution is X(t).

Now, I want to multiply X(t) by sin(y) and to plot in 3D.

How can we do it?

question.mw

## How do I select all system of equations have two...

I am trying to find the number a and b (-20 < a < 20, -20 < b <20) so that two circles (x+1)^2+(y+3)^2 = 125 and (x-a)^2+(y-b)^2 = 225 cut at two points A and B and coordinates A and B are pairs of integers.
I tried

restart; L := [];
for a from -20 to 20 do
for b from -20 to 20 do
for x from -20 to 20 do
for y from -20 to 20 do
if (x+1)^2+(y+3)^2 = 125 and (x-a)^2+(y-b)^2 = 225 and nops({a, b, x, y}) = 4 and x*y*a*b <> 0 then
L := {op(L), {[a, b], [x, y]}}
od: od: od: od:
nops(L);
L

How to select the number a and b so that the system of equations (x+1)^2+(y+3)^2 = 125  and (x-a)^2+(y-b)^2 = 225 have two integral solutions. For example

restart;
solve({(x-6)^2+(y+2)^2 = 225, (x+1)^2+(y+3)^2 = 125}, {x, y})

## numerical roots solver has problems?...

restart;

Digits := 32;

t0 := 1;

eq := 1-w*v^2-2*v*exp(-t/v);

equ := eval(eq, v = -t/ln(u));

us := solve(eval(equ, t = t0), u);

vs := -t0/ln(us);

plot(Re(vs), w = 0 .. 10, view = 0 .. 1)

I want to plot the solution of this equation, but it doesn't quite work. I tried to transform it, because I thought the singularity in the denominator of the exponential causes the issues.

any suggestions?

## implicit plot bu the x-axes is x/(2*Pi)...

Dear all.

Trying to plot the function below:

epsilon
f := ------- = 0.78417289325174246201875653872811303 + (
2 Pi
-24.020590879328464004990474127244023 + Y

(671.68643760557259657756434855357346 + (
-314.15926532756339731350799859659950 Y

- 48.382487297515945228479754993851165)^2))^(1/2)

want the (x-axis) be epsilon/(2*Pi) and the y-axis is Y
implicitplot(f,epsilon=0..100,Y=0..10,numpoints=1000,axes=boxed,thickness=2,color=black,font=[1,1,20],tickmarks=[3, 3],linestyle=1);

## Semantics of "->"?...

example1 := (x -> (2 + 3));
example2 := (x -> int(1, y));

When I execute these, Maple evaluates the "2 + 3" into 5, but it does not evaluate the "int(1, y)" into "y". Why does it evaluate the former but not the latter?

Also, how can I modifiy example 2 so that it evaluates the "int(1, y)" and returns "x -> y"?