## How do I solve a differential equation in Maple?...

By printing each processing step for a parametric surface entered in 3-dimensional space,

i- Finding whether the surface is a ruled(regle) surface and printing it in the ruled surface form,

ii- Calculating the dispersion parameter of the surface and the throat line,

iii- Draws the surface and the throat line on the surface together,

## CompositionSeries just work in transitive group?...

When I run this code, I will get a error information:

`CompositionSeries(SmallGroup(336, 209))`

It's mean this function just work in transitive group? But `IsTransitive(SmallGroup(336, 209)`) will get `true`. Is it a bug of maple? Or do I have any misunderstandings?

## densityplot legend...

Hi,

I am using the following (dummy) code to generate a density plot.

densityplot(x-y^2, x=-5..5, y=-5..5, axes=boxed, style=patchnogrid, numpoints=1000, legendstyle=[location=bottom], labels=[x, y]);

While this command does generate x vs y plots with varying color shared, I cannot figure out where the function (x-y^2) value by looking at the color shades. Is there a way to produce a legend along with the plot that will demonstrate how the function is taking different values with parameters?

I found a similar post, dated 2005, that suggests using the "s_tyle=" command. However, it does not work for some reasons. I would appreciate help in this regard.

Thank you,

Omkar

## Is it possible to filter a dataframe based upon a ...

I know you can filter a dataframe by putting constraints on the numeric columns. However, I would like to sort and filter based upon a given string in a column, is this possible? I cannot immediately find this in the help files. Thank you for your assistance.QuestionDataFrame.mw

## How to solve a cubic assuming discriminant conditi...

Hi MaplePrimes.

I have a cubic with some parameters that I would like to solve and recieve 3 real solutions, however I cannot seem to find a way to get that to work while using assumptions. I always recieve 1 real and two complex conjugate answers. I have tried assuming the discrimant to be greater then zero but nothing seems to be working, and I have looked through a few posts on here but I cant seem to find anything out. In particular solve({f,conditions},{variable})

If I solve with a known set of paramters(which i determine graphically) that gives three solutions everything works fine. Also if I solve the cubic generally and recieve the two complex solutions and one real then substitute the paramters in I get the same correct answers, so I am slightly baffled. If I have missed something simple my apologies.

Any help would be greatly appreciated. File attached.

CubicSolve.mw

## How to solve the given BVP using differential tran...

HI, I have numerically solved the given problem using the dsolve command But I want to solve the same problem using the Differential transformation method.
Can anyone help me to get the series solution for the given problem using DTM.

I want to compare the numerical results with DTM results when lambda =0.5.

eqn1 := diff(f(eta), `\$`(eta, 3))+f(eta)*(diff(f(eta), `\$`(eta, 2)))-(diff(f(eta), eta))^2-lambda*(diff(f(eta), eta)) = 0.

eqn2 := diff(theta(eta), `\$`(eta, 2))+f(eta)*(diff(theta(eta), eta))*Pr = 0

Bcs := (D(f))(0) = 1, f(0) = 0, (D(f))(infinity) = 0, theta(0) = 1, theta(infinity) = 0;

[lambda = .5, Pr = 6.3]

## Why does Maple not simplify to infinity?...

Evaluating this integral

 (1)

 (2)

produces an infinite product as output. Why does Maple not automatically simplify to infinity. Can the extra information (1+pi) be of any use?

## How to use sequence in a procedure...

Please how can I define two sequences in a procedure with two arguments?

ans:= Array([seq( [j, doCalc(j, u)], j=-2..0, 0.006, u=1..334)]):

The procedure is doCalc(j,u)  and I received this error: invalid input: seq expects between 1 and 3 arguments, but received 4

Find attached my complete code.Seq_Proc.mw

## Bernoulli DGL y' = y^4 * cos(x) + y*tan(x) how can...

Good Morning Guys,

Please, could somebody help me with my problem in Maple?

The expression y' = y^4 * cos(x) + y*tan(x) with start-value y(0) = 0.5 has the solution of 1/root(cos(x)^2 * 8*cos(x)-3 * sin(x),3).

If I try to solve it with this method dgl_2 := diff(y(x), x) = y(x)^4*cos(x) + y(x)*tan(x) I don't get the right solution. Is it possible to solve this expression with a Tutor app? step by step? If yes I would so happy to tell me how I can do that.

Thanks a lot and I wish you all a nice sunday and stay safe.

## ExcelTools / import cells as text when cell format...

Is there a way to importing cell values as text, and not numbers, when the cell is formatted as a text?

As far as I can see, a cell with the value "1" is always import as "1.0" in ExcelTools, regardless if the cell is formatted as text or something else in Excel.

Writing '1 in the Excel cell however leads to a text import in Maple, and will give "1", not "1.0".

There is one more thing that is strange in Excel. Even if the cell is formatted as a text, or the cell content is with a ' before the number, Excel will allow a calculation with that value. Text value 4 will give 5, if added 1.

## How to rectify the error while using HPM to coup...

Dear maple user how to rectify the error  in solving the coupled differential equation using homotropy perturbation method and direct differentiations and compare the two result by plotting the graphs :

```restart:
with(PDEtools):
L:=4:Nb:=1:Nt:=1:#k is some constant
f(x):=sum((p^i)*f[i](x),i=0..L):
g(x):=sum((p^i)*g[i](x),i=0..L):
HO1:=(1-p)*(diff(f(x),x,x))+p*(((1/x)*(diff(f(x),x))+Nb*((diff(f(x),x))*diff(g(x),x))+Nt(diff(f(x),x)^2))):
expand(%):
collect(%,p):
HO2:=(1-p)*(diff(g(x),x,x))+p*(((1/x)*(diff(g(x),x))+(Nb/Nt)*((diff(f(x),x,x))+(1/x)*diff(f(x),x)))):
expand(%):
collect(%,p):
HO2:=%:
declare(f(x),g(x),prime=x):
for i from 0 to L+1 do equa[1][i]:=coeff(HO1,p,i)=0 end  do:
for i from 0 to L+1 do equa[2][i]:=coeff(HO2,p,i)=0 end  do:
con[1][0]:=f[0](0)=(h(x)/64),(D(f[0]))(0)=0:
con[2][0]:=g[0](0)=-(k-h(x)^2/4),(D(g[0]))(0)=0:
for j from 1 to L do:
con[1][j]:=f[j](0)=h(x),(D(f[j]))(0)=0:
con[2][j]:=g[j](0)=h(x),(D(g[j]))(0)=0:
end do;
for i from 0 to L do;
dsolve({equa[1][i],con[1][i]},f[i](x));
f[i](x):=rhs(%);
f[i](x):=evalf(%);
dsolve({equa[2][i],con[2][i]},g[i](x));
g[i](x):=rhs(%);
g[i](x):=evalf(%);
end do;
for u from 0 to L-1 do:
f[u](_z1):subs(x=_z1,f[u](x));
g[u](_z1):subs(x=_z1,g[u](x));
f[u+1](x):=value(simplify(f[u+1](x)));
f[u+1](x):=simplify(%);
g[u+1](x):=value(simplify(g[u+1](x)));
g[u+1](x):=simplify(%);
end do:
f(x):=evalf(simplify(sum(f[n](x),n=0..L)));
#### direct calculations
#direct solve the two equations in terms of f(x) and g(x) for h(x)=e^x where Nt and Nb #are parameters and its takes some values example 1,1
restart:
with(DETools):
with(plots):
with(IntegrationTools):
Nb:=1:Nt:=1:h(x):=e^x:
Eq1 := (diff(f(x),x,x))+(((1/x)*(diff(f(x),x))+Nb*((diff(f(x),x))*diff(g(x),x))+Nt(diff(f(x),x)^2))):
Eq2 := (diff(g(x),x,x))+(((1/x)*(diff(g(x),x))+(Nb/Nt)*((diff(f(x),x,x))+(1/x)*diff(f(x),x)))):

Cd1 := f(0) = h(x), (D(f))(0) = 0:
dsys := {Cd1, Eq1}:
dsol := dsolve(dsys, numeric, output = operator):
#dsol(.1):
plots[odeplot](dsol, [x, diff(f(x), x\$1)], 0 .. 5, color = green):
Cd2 := g(0) = h(x), (D(g))(0) = 0:
dsys := {Cd1, Cd2, Eq1, Eq2}:
dsol := dsolve(dsys, numeric, output = operator):
plots[odeplot](dsol, [x, f(x)], 0 .. 5, color = red);
plots[odeplot](dsol, [x,g(x)], 0 .. 5, color = black);

```

## How to label the DrawSubgroupLattice with the orde...

This is the default style about the group of `DrawSubgroupLattice`:

`DrawSubgroupLattice(SymmetricGroup(4))`

But I hope to label the `DrawSubgroupLattice` with the order of the subgroup but not the default index, is it possible? I can get the order with this code:

`GroupOrder~(SubgroupLattice(SymmetricGroup(4), output = list))`

But I don't know how to label it into the node...

## How to replace a row of a matrix with the row of a...

How to replace 7th-row(second last) of the matrix H116 (see eq. (14)) with the 1st-row of the matrix H16 (see eq. (15)) and create a new matrix of size same as H116?

matrixop.mw

## Trouble with multiple quotes in data entry...

I've run into a problem.  I'm trying to enter multiple quotes in a string.

for example

a:=[["{"test1","test2"}"],["{test3","test4"}"]]

## Why plot(F(R), R = 0 .. 100) doesn't work?...

How to plot F(R) for R=0..100 ?

Maple 2021 sheet attached.

 (1)

 (2)

 (3)

 (4)