## Writing the wave pde solution ...

Writng the Pde wave function solution in a textbook form ?
golfvergelijking_oplossing_gebruiken_om_integraaluisom_te_halen_voorbeeld.mw

## Maple densityplot: "scaletorange" option doesn't w...

Below is the code in Maple 2022, and then I describe the problem.
restart;
with(plots);
a := 0.5;
j := BesselJ(0, sqrt(2*I)*sqrt(x^2 + y^2)*a)/BesselJ(0, sqrt(2*I)*a);
A := sqrt(Re(j)^2 + Im(j)^2);
densityplot(A, x = -1 .. 1, y = -sqrt(-x^2 + 1) .. sqrt(-x^2 + 1), grid = [68, 68], style = patchnogrid, scaletorange = 0 .. 1);

Thus, I have a real function of two variables: \$A(x, y)\$. At zero it is minimal (value 0.996). At the boundary of the unit circle it is maximal with a value equal to 1. In theory, scaletorange = 0 .. 1 should give a picture with almost perfectly white everywhere in the circle since the function values â€‹â€‹are very close to 1. However, both with scaletorange and without it, the command produces a picture with a significantly dark circle in the center...

## Can plot plot with colorfunctions ...

I am looking for something similar to color functions of plot3D. plot.options is directing me to plot,color where I cannot find an example. I tried

```plot(floor(x),x=-3..3,color=floor(x))

Error, (in plot) invalid color specification: floor(x)
```

## Arrange the list elements...

Suppose I have a list of differential equations:

L:=[x*diff(f(x),x)+2*x+1=0, 4*(diff(f(x),x\$2))^2+7*diff(f(x),x)-2=0, x*diff(f(x),x)+2*x+1=0, 3*(diff(f(x),x))^2-f(x)-1=0];

how can I rewrite this list such that
L:=[[x*diff(f(x),x)+2*x+1=0,2], [4*(diff(f(x),x\$2))^2+7*diff(f(x),x)-2=0,1], [3*(diff(f(x),x))^2-f(x)-1=0,1]];
i.e., rewrite this list as the [equation, Number of occurrences in the list]

## Solve an equation with unknown expression...

Hi all guys, it is simple equation, I wanna get the expression of w=()^(1/4) which consists zg & fg. I use solve command but fails, could you please help me?

 >
 (1)
 >
 (2)

## has always returns false...

Dear all, why "has" always returns false ?

## Why assignment type mismatch can not be cought by ...

I do not know if this is how it always been in Maple. But now I noticed when I set assertlevel to 2, in order to catch wrong assignment type in my code, the try/catch do not catch such an error.

My question is: Has it always been like this in Maple? May be it was, I am just asking for confirmation. I seem to remember I was able to trap such error before.

Here is MWE

 > interface(version);

 > Physics:-Version();

 > libname;

 > restart;
 > interface(warnlevel=4): kernelopts('assertlevel'=2):
 >
 > foo:=proc(); local C_sol::list;    try       C_sol := 1;    catch:       print("error detected in my code");    end try; end proc:
 > foo(); #unable to catch assignment error

Error, (in foo) assertion failed in assignment to C_sol, expected list, got 1

## Read in Maple Code Attachments...

I'm struggling getting read statements to work in code attachments.

Are there any limitations for the read command?

Test.zip

## a problem in change of variables...

Hi dear mapleprime users, i have a problem in a change of varibales if the following ode. i want to use "r=R*rs,u(r)=h*u(R*rs)" variable changes in ode, how can i do that, R is a constant. tnx for the help

 > restart;with(Student[ODEs]):
 > y := (1 + diff(u(r), r))*diff(u(r), r, r) + (1 + vs*u(r)/r + (1 - vs)/2*diff(u(r), r))*diff(u(r), r)/r - (1 + (1 + vs)/(2*r)*u(r))*u(r)/r^2
 (1)
 > constants := constants, R:
 > subs(r=R*rs,u(r)=h*u(R*rs),y) ;convert(%,D)

## what is the correct syntax for setting initial con...

I sort of remember there is a special syntax for setting initial condition for an ode derivative as    y'(a)=b, where and are symbols. I forgot what it is, everything I try gives error. (I thought eval was used to work for this, but can't get it to work now).

Any one knows how to set this IC?   For an example, given this ode y''(x)+y'(x)+y(x)=0 I want to solve it with the IC as   y'(a)=b where has no numerical value. Just a symbol.

For an example, using another software, it is done as follows

```ClearAll[x,y,a,b];
ode=y''[x]+y'[x]+y[x]==0;
DSolve[{ode,y'[a]==b},y[x],x]```

Below is my attempts in Maple. I tried eval, subs, and the normal D(y)(a)=b but none of these works when is symbol.

I looked at help and all examples I saw use constants, as in D(y)(0)=value.

Iam sure this is possible to do in Maple, but I forgot how. Below is worksheet.

 > interface(version);

 > restart;
 > ode:=diff(y(x),x\$2)+diff(y(x),x)+y(x)=0; IC1:=eval(diff(y(x),x),x=a)=b; IC2:=D(y)(a)=b; IC3:=subs(x=a,D(y)(x)=b);

 > dsolve([ode,IC1]);

Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {y(a), y(x)}

 > dsolve([ode,IC2]);

Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {y(a), y(x)}

 > dsolve([ode,IC3]);

Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {y(a), y(x)}

 > #eval works if the point is actual value as in IC1:=eval(diff(y(x),x),x=0)=b;

 > #but I want x=a in the above.

There is no issue for dirichlet initial condition, where  y(a)=b works. It is the  neumann one which I can't figure its syntax. So this works OK

```ode:=diff(y(x),x\$2)+diff(y(x),x)+y(x)=0;
IC1:=y(a)=b;
dsolve([ode,IC1]);
```