## What is the technique of getting conditionaly solu...

What is the idea  of getting equation (48),(49), and (50)

## Factoring in long ODE and find parameters in bette...

I find thus equation of course i use a little bit seperation by hand, i have 11 equation but i can't get results of parameters i don't know why my code is a little bit old i think and i don't know there is another technique for finding them or not here is the file of mp, thanks for any help

F_P_Correct.mw

for apear each part  remove (:)

## Single pendulum sweep frequency analysis...

Change the length of the pendulum to achieve the analysis of the pendulum frequency change, but I scan the frequency of the two images do not correspond to each other, what is the problem?

sweep.mw

## Extend/Truncate list of Colours to plot ...

I need to automatically extend or truncate a colour list to suit number of points in plottools:-point plot.
extending the list the colour sequence could be repeated or if the is too awkard just add black.
I can't figure out how to select the list of colours to put into a new list to modify.

This will be inside a plotting procedure.

 > restart
 > with(ListTools)
 (1)
 > L:=[[1,2],[3,4],[-5,6],[-3,-2]]
 (2)
 > qty:=nops(L)
 (3)
 > styles:=[symbol=solidcircle,colour=[red,green,blue,orange],symbolsize=12]
 (4)
 >
 > plots:-display(plottools:-point(L,styles[]))
 > #Need to extend or truncate the list of colours to match the number of points #styles can be copied to styles 1,2 etc #the extended list would be a repeatition of the colour sequence given #would need to look for color or colour; has(styles,colour); #how to select colour our into a seperate list?
 (5)
 > #too few point for the colours; L1:=[[1,2],[3,4],[-5,6]]
 (6)
 > plots:-display(plottools:-point(L1,styles[]))
 > #too many point for the colours; L2:=[[1,2],[3,4],[-5,6],[-3,-2],[6-1],[0,1]]
 (7)
 > plots:-display(plottools:-point(L2,styles[]))

## Min is bigger than max???...

Hello

in this example Untitled.mw Maple 2022 on MacOs  'finds' a minimum bigger than the maximum.

It looks like something is wrong...

Best Nicola

## How do I mute the action of an accent applied to a...

How do I mute the action of an accent applied to a symbol so that the accented symbol is itself an inert object? See the attached example.

How_do_I_make_an_accented_symbol_inert.mw

## Diophantine equation...

As a newbie in Maple2024, my next step is to try to solve a Diophantine equation. Attempts with isolve failed. It is the famous task B3 from the IMO of 1988:

If for integers x and y the fraction (x^2+y^2)/(1+x*y) is a positive integer, then it is actually a square number.

The solution is well known. But I would like to learn how to use Maple using this example and would like some advice.

Best regards, Alfred_F

## PDEtools/NumerDenom internal error when calling od...

I was trying to odetest one of my solutions to this ode when I got this internal Maple error I have not seen before.

Is this a legitimate error? my solution could be wrong ofcourse but strange to get internal error in this case.

Does this happen on earlier versions of Maple?

 > interface(version);

 > Physics:-Version();

 > libname;

 > restart;
 > sol:=Intat(1/(u^n/((1/((a*g(x)+b)^n)/(f(x)^n)*diff(g(x),x)*f(x))^(-n-1))/((f(x)*diff(g(x),x))^(-2*n+1))/((1/((a*g(x)+b)^n)/(f(x)^n)*diff(g(x),x)*f(x)*(diff(f(x),x)*diff(g(x),x)+f(x)*diff(diff(g(x),x),x))-(-1/((a*g(x)+b)^n)/(f(x)^n)*diff(g(x),x)^2*f(x)*n*a/(a*g(x)+b)-1/((a*g(x)+b)^n)/(f(x)^n)*diff(g(x),x)*n*diff(f(x),x)+1/((a*g(x)+b)^n)/(f(x)^n)*diff(diff(g(x),x),x)*f(x)+1/((a*g(x)+b)^n)/(f(x)^n)*diff(g(x),x)*diff(f(x),x))*f(x)*diff(g(x),x)-f(x)*diff(f(x),x)/((a*g(x)+b)^n)/(f(x)^n)*diff(g(x),x)^2*n)^n)/(n^(-n))-u+1),u = a/f(x)/(a*g(x)+b)*y(x))-ln(a*g(x)+b)+_C1 = 0;

 > ode:=diff(y(x),x)-f(x)^(1-n)*diff(g(x),x)*y(x)^n/((a*g(x)+b)^n)-diff(f(x),x)*y(x)/f(x)-f(x)*diff(g(x),x) = 0;

 > odetest(sol,ode,y(x));

Error, (in PDEtools/NumerDenom) invalid input: PDEtools/NumerDenom expects its 1st argument, ee, to be of type Or(algebraic,table,rtable), but received {Intat(1/(u^n*(f(x)^(1-n)*diff(g(x),x)*(a*g(x)+b)^(-n))^n*(f(x)*diff(g(x),x))^(2*n)*n^n-u*(a*g(x)+b)^n*f(x)^n*(a*n*f(x)^(2-n)*diff(g(x),x)^3*(a*g(x)+b)^(-n-1))^n+(a*g(x)+b)^n*f(x)^n*(a*n*f(x)^(2-n)*diff(g(x),x)^3*(a*g(x)+b)^(-n-1))^n),u = _Z) = Intat(1/(u^n*(f(x)^(1-n)*diff(g(x),x)*(a*g(x)+b)^(-n))^n*(f(x)*diff(g(x),x))^(2*n)*n^n-u*(a*g(x)+b)^n*f(x)^n*(a*n*f(x)^(2-n)*diff(g(x),x)^3*(a*g(x)+b)^(-n-1))^n+(a*g(x)+b)^n*f(x)^n*(a*n*f(x)^(2-n)*diff(g(x),x)^3*(a*g(x)+b)^(-n-1))^n),u = _Z)}

## Is there a way to re-index an existing dataframe?...

Is there a way to re-index an existing dataframe? See attachment for example.

how_do_i_re-index_a_dataframe.mw

## Can someone help me open this file?...

So I have this Maple document that I worked on yesterday, and now when I open it it just opens as the start-up screen where I can choose between document and worksheet mode. I can see that the file is much larger (900 kb) than an empty document, so it should definitely have the data still in there, but opening it with a text editor I couldn't manage to fix my issue. Does anyone have any tips? I have a back-up of the file (from the restore backup menu), but most of the content is not there, so it would be very helpful to get this one fixed.

Exercises.mw
Kristian.

## Circle of maximum radius inscribed between curves...

The problem arose while playing with inscribed circles, as in this post. If anyone is interested, try to find a circle of maximum radius inscribed between the curves
x1^2 + 2*x2^2 - 1 = 0 and (x1 - sin(x1))^2 + (x2 - sin(x2))^2 - 1 = 0.

Curve graphs.

## Idea of use changing Rule by using ODE ...

By using the second order ODE and its solution how i can get thus changing Rule?  i am looking for equation (8) by assumption of the paper he did, there is a trick but i don't know

idea.mw

## How can find dihedral angle of two halfplanes?...

I see here
https://mathematica.stackexchange.com/questions/306634/how-can-i-use-dihedralangle-to-get-correct-result/306638?noredirect=1#comment751373_306638

Let $S.ABCD$ be a pyramid, $ABCD$ is a square with $AB = 1$. The line $SA$ perpendicular to the plane $ABC$.

Calculate dihedral angle of two halfplanes SBC and SCD if: $SA = 1$, $SA = \dfrac{\sqrt{2}}{2}$.  I tried
restart;
with(Student:-MultivariateCalculus);
a := 1;
h := 1;
pA := [0, 0, 0];
pB := [a, 0, 0];
pC := [a, a, 0];
pD := [0, a, 0];
pS := [0, 0, h];

## Fit Equation to Data...

I am attempting to obtain an equation for battery discharge.

I have data from a battery that will supply 25 amps for 210 minutes. I want to fit this to an equation and then try to adjust the curve to match a battery that will supply 25 amps for 160 minutes.

Here is what I have:

restart; with(Statistics):

## Amps
A := Vector([444, 218, 74,312/10,209/10,119/10,625/100]):
## Time until battery discharges to 10.5 volts
T := Vector([5,15,60,3*60,5*60,10*60,20*60]):
f := x -> a*exp(1-x/b); f(x)
eqset := {seq(T[idx] - f(A[idx]), idx=1..7)}
sol := NonlinearFit(a*exp(1-x/b),A, T, x)
evalf(subs(x=A[6],sol))
P1 := plot(A,T): P2 := plot(sol,x=0..450): plots[display]({P1,P2})

I want the 'knee' of the fitted curve to more closely match the measured data.

How do I do this?