Solving differential equations, Maple sometimes unfortunately returns the solution in an utterly  unusable form I never encountered a use for.

As an example a solution was found assuming separation of variables. Maple returns the following solution,

Is there a command where I can just get the argument of the solution, namely the differential equation diff(_Y(ts),ts,ts) + etc  ?  or even better as diff(X(ts),ts,ts) + etc   as I intended and expected it to be without the silly and unnecessary proxy variable _Y(ts) ?

It is such a pity that Maple return these results not as a differential equation in F2(ts), but gives the result in a proxy variable which isutterly unnecessary.

Anyway, if anyone knows a command just to get the argument of the solution above to get rid of all the unnecessary and proxy structure, I will appreciate it as I currently copy the solution and redefine it, which can introduce errors and destroys the generality of the document.

A classic result states that the equation x³＋px²＋qx＋r＝0 with real coefficients p, q, r has positive roots iff p＜0, q＞0, r＜0 and -27r² - 2p(2p² - 9q)r + q²(p² - 4q) ⩾ 0 (see for example this question). 
However, Maple appears unable to find the condition: 

a, b, c := allvalues(RootOf(x^3 + p*x^2 + q*x + r, x), 'implicit'):
RealDomain:-solve({a, b, c} >~ 0, [p, q, r]);
 = 
Warning, solutions may have been lost
                               []

Is there a way to get the above conditions in Maple with as little human intervention as possible (I mean, without a priori knowledge of the theory of polynomials)? 

Edit. An interesting problem is when these three positive roots can further be the lengths of sides of a triangle. For reference, here are some (unenlightening) results from some other software: 

I don't know how make my graph be beter for real part and imaginary part and abs part which part how work with parameter can any one explain on this example?

G.mw

I have this file
 

restart:
F := proc(ee,LL)
  uses InertForm, Typesetting;
  mrow(Typeset(Display(eval(eval(MakeInert(factor(ee)),[`%*`=`*`])
                                 =MakeInert(subs(b=MakeInert(b*y)/y,
                        a=MakeInert(a*x)/x,p)),[a,b]=~LL),
                       inert=false)),
       mo("="),Typeset(eval(ee,[a,b]=~LL)))
end proc:
p := (a*x)^2 - 2*a*x*b*y + (b*y)^2:
L := [[sqrt(2),3],[2,5],[3,12],[1/3,5/7]];
ans := F~(p, L):
print~(ans):

How can I put the results like this
 

\documentclass[12pt,a4paper]{article}
\usepackage[left=2cm, right=2cm, top=2cm, bottom=2cm]{geometry}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{enumitem}
\theoremstyle{definition}
\newtheorem{ex}{Exercise}
\begin{document}
\begin{ex}
\[(\sqrt{2} x-3 y)^2=(\sqrt{2} \cdot x)^2-2 \cdot(\sqrt{2} \cdot x) \cdot(3 \cdot y)+(3 \cdot y)^2=2 x^2-6 \sqrt{2} x y+9 y^2.\]
\end{ex}

\begin{ex}
\[(2 x-5 y)^2=(2 \cdot x)^2-2 \cdot(2 \cdot x) \cdot(5 \cdot y)+(5 \cdot y)^2=4 x^2-20 x y+25 y^2. \]
\end{ex}

\begin{ex}
\[(3 x-12 y)^2=(3 \cdot x)^2-2 \cdot(3 \cdot x) \cdot(12 \cdot y)+(12 \cdot y)^2=9 x^2-72 x y+144 y^2. \]
\end{ex}

\begin{ex}
\[\left(\frac{x}{3}-\frac{5 y}{7}\right)^2=\left(\frac{1}{3} \cdot x\right)^2-2 \cdot\left(\frac{1}{3} \cdot x\right) \cdot\left(\frac{5}{7} \cdot y\right)+\left(\frac{5}{7} \cdot y\right)^2=\frac{1}{9} x^2-\frac{10}{21} x y+\frac{25}{49} y^2. \]
\end{ex}
 
\end{document} 

The attached sheet contains equations H1 to H6 and K1 to K3. What data do I need to modify to ensure that the values of H1 to H6 fall between 0 and 1, and K1 to K3 are negative? The parameter ranges are also given in the sheet. Is there a method to achieve this?

rouhg.mw

i did two case of this equation and odetest is worked good but in this case the odetest is not worked well anyone can determine what is mistake ?

F_P_Correct_case_three.mw

Dear Maple user I am facing error while running the codes  to plot the graph for two data sets .

I am attaching the files.

Error_in_Display_1.mw

Why does dsolve not call odetest by default before a solution is returned?

I mean, why do I have test each result separately. dsolve could have an odetest option (default=true).

In case of discrepancies dsolve could inform the user and suggest to call dsolve with odetest=false and run odetest separately to analyse the problem.

Set up this way, dsolve would never return potentially incorrect solutions that do not pass odetest.

HTR.mw

In above problem, Additionally How to  plot  heat transfer rate  Q versus L^2  for distinct porosity parmeters(Sh) , using  heat transfer rate formula, Q = (q*L)/(k*A*T[b])=theta'(1).

using  [Sh = 0.1, L^2 = 0.1, Nr =0 .1, Ha =0 .1, Pe = 0.1],  [Sh = 0.3, L^2 = 0.3, Nr = 0.1, Ha = 0.1, Pe =0 .1],   [Sh = 0.5, L^2 =0 .5, Nr =0 .1, Ha = 0.1, Pe =0 .1].

How can I find Mean, Median, Quartiles, Variance, StandardDeviation of data in this table

I use Mathamatica and get the result

Clear["Global`*"]
boundaries = Range[0, 10, 5/2];
frequencies = {18, 11, 13, 6};
binMeans = Mean /@ Partition[boundaries, 2, 1];
weighted = WeightedData[binMeans, frequencies];
weightedHist = HistogramDistribution[weighted, {5/2}];
Through[{Mean, Median, Quartiles, Variance, StandardDeviation}[
  weightedHist]]

I trying to simplify expressions for lines so no higher order terms. factor and op seperate out what I need but how do I select the one with the variables in this case x,y. I cant depent on this always been the last one returned from the op command.

Download 2024-09-11_Has_Select_Question.mw

I get my on results but the results are not the same please help me if i did any mistake in my code

symmetry_PDESYS_3_time_fraction[1].mw

This code is working for function f1 but not for f2
f2 := (x,y)->9*x^2-24*x*y+16*y^2+10*x-70*y + 175;
Why this code is not working for f2 ?
unprotect(D);
f1:= (x, y) -> 3*x^2 - 3*y*x + 6*y^2 - 6*x + 7*y - 9;
coeffs(f(x, y));
A, B, C, D, E, F := %;
theta := 1/2*arctan(B/(A - C));
solve({-2*A*xc - B*yc = D, -B*xc - 2*C*yc = E});
assign(%);
x := xcan*cos(theta) - ycan*sin(theta) + xc;
y := xcan*sin(theta) + ycan*cos(theta) + yc;
Eq := simplify(expand(f1(x, y)));
xcan^2/simplify(sqrt(-tcoeff(Eq)/coeff(Eq, xcan^2)))^`2` + ycan^2/simplify(sqrt(-tcoeff(Eq)/coeff(Eq, ycan^2)))^`2` = 1;

Thank you

I'm trying to solve a system of coupled differential equations numerically, but I'm getting the following error

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

The error occurs at the dsolve step, despite trying to ensure that all equations and conditions are in the correct form (sets/lists).

Could someone help me identify what I'm missing here?

Thanks in advance!

Download dsolve_error.mw