I am trying to solve the following ode in Maple. Here is the code below 

dsolve(diff(b(x), x, x, x)/2 + diff(b(x), x, x)/x + 2*diff(b(x), x)/(x^2 + 1)^2 - 4*x*b(x)/(x^2 + 1)^3 = 0)

and the output I get is the following:

b(x) = DESol({-8*x^2*_Y(x) + (4*x^3 + 4*x)*diff(_Y(x), x) + (2*x^6 + 6*x^4 + 6*x^2 + 2)*diff(_Y(x), x, x) + (x^7 + 3*x^5 + 3*x^3 + x)*diff(_Y(x), x, x, x)}, {_Y(x)})

I don't understand what the function _Y(x) means. Could someone please explain? 

Thanks in advance!  

For example for an ellipsoid with principal axes 3, 2 and 1 along the x, y and z coordinate axes respectively, with center at the origin and truncated at x equals 1.

What math will reveal its center of mass and its moment of inertia for an axis of revolution through the center of mass and parallel to the y axis?

I am trying to vopy paste a table of 10*20 from maple sheet to ms word but failed. His their any special way of copying tables from maple sheet to ms word without formating chnages?

Please, how can I find all the roots  of: (H/(Hc))^2 -(4*q^2)/Pi^2*((tan(q)- q/(1-alpha))/(tan(q)-q)) with q=(i-1)*Pi+Pi/2..i*Pi+Pi/2 for n=20.

See my attempt below:

restart:with(RootFinding):
a[1] := .1093; k[3] := 7.5*10^(-12); k[2] := 3.8*10^(-12); d := 0.2e-3; eta[1] := 0.240e-1; alpha[2] := -.1104; alpha[3] := -0.1104e-2; eta[2] := .1361; xi := 1.219*10^(-6); alpha := 1-alpha[3]^2/(a[1]*eta[1]); theta[0] := 0.5e-1;
Hc := (Pi/d)*sqrt(k[2]/xi):

H := 5.5*Hc;
lambda := a[1]/(xi*H^2);

RootFinding:-NextZero(proc (q) options operator, arrow; (H/(Hc))^2 -(4*q^2)/Pi^2*((tan(q)- q/(1-alpha))/(tan(q)-q)) end proc, 0);

for j to 9 do RootFinding:-NextZero(proc (q) options operator, arrow; H^2/Hc^2-4*q^2*(tan(q)-q/(1-alpha))/(Pi^2*(tan(q)-q)) end proc, %) end do;

Error, invalid input: RootFinding:-NextZero expects its 2nd argument, zz, to be of type numeric, but received FAIL

Hi

I wanted to know how to search a list of permutations given criteria: print the permutation(s) If the 4th element of each perm was equal to [C,Z} and the seventh was equal to [B,Y]

perm.mw

Hello, 

I have an equation in the form:

x(t)=2*a+b*t+2*t;

where a and b are the unknowns that I have to find. 

my initial conditions are x(0)=1 and x(1)=1. How can I solve this equation in maple?

Thank you very much for your help!

So all I'm trying to do is a simple sequence like seq(i^2, i=1..10, 1) but with units.  The seq function is part of the Units:-Standard and Units:-Simple packages.  I couldn't find any examples with units in the help system.  For my first attempt, I tried to create a simple sequence of values with units using what is, to me, a logical syntax.  I have included the Maple input below.  I bolded the input.

with(Units:-Standard);
[*, +, -, /, <, <=, <>, =, Im, Re, ^, abs, add, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, 

  arcsinh, arctan, arctanh, argument, ceil, collect, combine, conjugate, cos, cosh, cot, coth, csc, csch, csgn, diff, eval, 

  evalc, evalr, exp, expand, factor, floor, frac, int, ln, log,  log10, log2, max, min, mul, normal, polar, root, round, sec, 

  sech, seq, shake, signum, simplify, sin, sinh, sqrt, surd, tan,   tanh, trunc, type, verify]

seq(ii, ii = 1.0*Unit('m') .. 10.0*Unit('m'), 1.0*Unit('m'));

Error, (in Units:-Standard:-seq) wrong number (or type) of parameters in function seq

Can anyone show me the correct syntax for this?  Is there something in the help?  I tried it in 2021 and 2022 with the same result.
 

Is it possible to read and/or convert Mapleflow sheets to Maple?

This is the first time I see such an error installing Maple on windows.

Right after the MS VS run-time installation completed (which is started by Maple installer) I got an error message saying it could not install fonts and to install them "manually".

Are there detailed instructions how is one supposed to do this? And what does this actually affect? As Maple starts ok and so far I see no issue with fonts but I have not done much with it yet other than open a worksheet and type few commands.

Looking at the folder in question, I see no instructions. Only font files. It will be good if Maplesoft could provide instructions for users on how to do that.  I do not want to do something that could end breaking the Maple installation or make things worst.

Does anyone know how to make a command for Leibniz formula for pi?

I would preferably like to use: 1-1/3+1/5-1/7+1/9..=pi/4

I don't want to sit and write everything out, but would like to make it a command, and decide myself how many calculations I would like. I have no clue how though. Anyone have an idea for that?

restart;
with(LinearAlgebra):
a := .1093;
b[3] := -0.1104e-2;
k[1] := 3.8*10^(-12);
d := 0.2e-3;
xi := -1;
theta0 := 0.1e-3;
eta[1] := 0.240e-1;
alpha := 1-b[3]^2/(a*eta[1]);
c := b[3]*xi*alpha/(eta[1]*(4*k[1]*q^2/d^2-b[3]*xi/eta[1]));

f:= q-(1-alpha)*tan(q)- c*tan(q) ;
plot(f,q=0..4*Pi,view=[DEFAULT,-1..10]):

   
n:=3: 
q[1]:=fsolve(f,q=(0..Pi/2)): 
for i from 2 to n do
q[i]:=fsolve(f,q=(2*i-3)*Pi/2..(2*i-1)*Pi/2): ##q[n]
od:

printlevel := 2;
for i from 2 to n+1 do for j from i+1 to n do b[i, j] := int((cos(q[i]-2*q[i]*z/d)-cos(q[i]))*(cos(q[j]-2*q[j]*z/d)-cos(q[j])), z = 0 .. d); b[j, i] := b[i, j] end do end do;

for i from 2 to n do a[i, i] := int((cos(q[i]-2*q[i]*z/d)-cos(q[i]))*(cos(q[i]-2*q[i]*z/d)-cos(q[i])), z = 0 .. d) end do;

for i from 2 to n do f[i] := theta0*(int(cos(q[i]-2*q[i]*z/d)-cos(q[i]), z = 0 .. d)) end do;

## I have generated a matrix using the a[i,i] above
A := Matrix([seq([seq(a[i, j], i = 2 .. n)], j = 2 .. n)]);

b := Vector([seq(f[i], i = 2 .. n)]);
     

#Please, how do I generate an upper triangular matrix using b[i,j] above?        

I am using Maple 2021.2 on Ubuntu Linux 20.04 LTS. Sometimes the Maple after start does not show Sig in part of top Maple desktop panel. So I need to restart Maple and 2nd or 3rd start is mostly OK. After that is the situation for some time good.

See attached snapshot... Any idea what is wrong?

hallo every body 

please how i do find a real roots for this equation system 

roots.mw

I set infolevel[dsolve]:=2; and first time I use it, it gives very long output. Next time I use it on same ode with same command it gives much shorter output.

Why is that and how to make it give the shorter output from first call?  This is very strange behavior.  One would expect the same output each time. The worksheet attached shows that first time it is used, the output is very long. At the end of the worksheet the call is made again with same infolevel, and now output is much smaller.

(getting error uploading worksheet. Will try again. Unable to do insert content keep getting error from this site. So I am just attaching it as link. May be due to large size of the worksheet)

infolevel_changes.mw

In a video (watch from 7 min onwards) I have seen the definition of solution types in custom components. Is this possible in newer versions of MapleSim using the custom component app? If yes, how?