## solve and dsolve commands...

I am newcommer in Maple. I am using Maple 2019. Just a simple question;

solve(x^2-3*x+4=0, x);

gives

1.50000000000000 + (9.09238836013723*10^(-59))*I, 1.50000000000000 - (9.09238836013723*10^(-59))*I

instead I need to show in the forms of radiacal. I have also the problem in dsolve command;

dsolve(2*diff(y(x),x\$2)+3*diff(y(x),x)+4*y(x),y(x));

with the result

y(x) = (2.73949338633639*10^(-116) + (2.73949338633639*10^(-116))*I)*_C1 + (1. + (2.73949338633639*10^(-116))*I)*_C2

Sayed

## how to do that?...

Considering the follwoing expr:

A(x):=mue+(mun/gama)+(u0^2)-mud*x-mue*exp(x)-(mun/gama)*exp(gama*x)-(u0^2)*(1-2*x/u0^2)^(1/2);

where

mue:=1/(1+alpha+beta);
mun:=alpha/(1+alpha+beta);
mud:=beta/(1+alpha+beta);
u0:=(mue+mun*gama)^(-1/2);
and assuming the values of alpha and beta lie between 0.1..0.6 and gama=15 ro 20.

How do I determine those values of (alpha,beta,gama) satisfying conditions [(3), (4)], [(3), (5)] or [(3),(6)]?

conditions:

A(x[m] <> 0) = 0:

where x_m is an extreme point of A(x) (other than x=0),

d*A(x)/dx, x = x[m] < 0:

d*A(x)/dx, x = x[m] > 0:

d*A(x)/dx, x = x[m] = 0:

## Special Integral...

f(x) = tanh(x)/sqrt(x^2+1)

limits x_initial =1, x_final =100

Thanks

## How to get all the types a variable verifies?...

Hi,

Does it exist a way to get all the types a variable verifies?
For instance
x:=4;
type(x, t); # true for t in {positive, posint, algebraic, ...}

## Simplifying a polynomial!...

Hi,
How do I simplify the following polynomial:

-(729 beta (1/2 (-1/9 (-5/27 beta-1/9) lambda^6-1/9 (1/9 beta^2 TT+(10/9 TE+2/3 TT) beta-1/9 TE) lambda^4+5/27 (2/5 TT (3/2 TT+TE) beta+TE (TE-2/5 TT)) beta lambda^2-1/9 TE beta^2 TT (-TT+TE)) p1(m,t)^2+(beta TT-1/3 lambda^2)^2 (-1/3 lambda^2+TE)^3 ((p2(m,t))/(lambda^2-3 TE)+3/2 ((lambda^2+TE) p1(m,t)^2)/((lambda^2-3 TE)^3))))/((3 beta TT-lambda^2)^3 (3 TE-lambda^2)^2),

as follows:

-3*beta*p2(m,t)/(lambda^2-3*beta*TT)+3*beta^2*(5*lambda^2-3*beta*TT)*p1(m,t)^2/(2*(lambda^2-3*beta*TT)^3)
?

## fix the problem to solve polynomial...

restart;
solve({l*(2*l^2*lambda^4*sigma*w*a[2]+l^2*lambda^2*mu*w*b[1]+6*l*lambda^2*m*sigma*a[0]^2-6*l*lambda^2*m*b[1]^2+6*l*m*mu^2*a[0]^2-l*lambda^2*rho*sigma*a[0]-l*mu^2*rho*a[0]+4*lambda^2*sigma*w*a[0]+4*mu^2*w*a[0]) = 0, l*(2*l^2*lambda^3*sigma*w*a[1]+6*l^2*lambda^2*mu*w*b[2]+2*l^2*lambda*mu^2*w*a[1]+12*l*lambda^2*m*sigma*a[0]*a[1]-12*l*lambda^2*m*b[1]*b[2]-l*lambda^2*rho*sigma*a[1]+12*l*m*mu^2*a[0]*a[1]-l*mu^2*rho*a[1]+4*lambda^2*sigma*w*a[1]+4*mu^2*w*a[1]) = 0, l*(5*l^2*lambda^3*sigma*w*b[2]-3*l^2*lambda^2*mu*sigma*w*a[1]-7*l^2*lambda*mu^2*w*b[2]-3*l^2*mu^3*w*a[1]+12*l*lambda^2*m*sigma*a[0]*b[2]+12*l*lambda^2*m*sigma*a[1]*b[1]-l*lambda^2*rho*sigma*b[2]+24*l*lambda*m*mu*b[1]*b[2]+12*l*m*mu^2*a[0]*b[2]+12*l*m*mu^2*a[1]*b[1]-l*mu^2*rho*b[2]+4*lambda^2*sigma*w*b[2]+4*mu^2*w*b[2]) = 0, l*(8*l^2*lambda^3*sigma*w*a[2]+6*l^2*lambda*mu^2*w*a[2]+12*l*lambda^2*m*sigma*a[0]*a[2]+6*l*lambda^2*m*sigma*a[1]^2+l^2*lambda*mu*w*b[1]-6*l*lambda^2*m*b[2]^2-l*lambda^2*rho*sigma*a[2]+12*l*m*mu^2*a[0]*a[2]+6*l*m*mu^2*a[1]^2-6*l*lambda*m*b[1]^2-l*mu^2*rho*a[2]+4*lambda^2*sigma*w*a[2]+4*mu^2*w*a[2]) = 0, -l*(4*l^2*lambda^3*mu*sigma*w*a[2]-l^2*lambda^3*sigma*w*b[1]+l^2*lambda*mu^2*w*b[1]-12*l*lambda^2*m*sigma*a[0]*b[1]+l*lambda^2*rho*sigma*b[1]-12*l*lambda*m*mu*b[1]^2-12*l*m*mu^2*a[0]*b[1]+l*mu^2*rho*b[1]-4*lambda^2*sigma*w*b[1]-4*mu^2*w*b[1]) = 0, 6*l^2*(l*lambda^2*sigma*w*a[2]+lambda^2*m*sigma*a[2]^2+l*mu^2*w*a[2]+m*mu^2*a[2]^2-lambda*m*b[2]^2) = 0, 2*l^2*(l*lambda^2*sigma*w*a[1]+6*lambda^2*m*sigma*a[1]*a[2]+3*l*lambda*mu*w*b[2]+l*mu^2*w*a[1]+6*m*mu^2*a[1]*a[2]-6*lambda*m*b[1]*b[2]) = 0, -2*l^2*(5*l*lambda^2*mu*sigma*w*a[2]-l*lambda^2*sigma*w*b[1]+5*l*mu^3*w*a[2]-6*lambda^2*m*sigma*a[1]*b[2]-6*lambda^2*m*sigma*a[2]*b[1]-l*mu^2*w*b[1]-6*lambda*m*mu*b[2]^2-6*m*mu^2*a[1]*b[2]-6*m*mu^2*a[2]*b[1]) = 0, 6*l^2*b[2]*(l*w+2*m*a[2]) = 0}, {a[0], a[1], a[2], b[1], b[2]});
Warning, solutions may have been lost
{a[0] = 0, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0},

/       l rho - 4 w                                        \
{ a[0] = -----------, a[1] = 0, a[2] = 0, b[1] = 0, b[2] = 0 }
\          6 l m                                           /

## Cannot open Incomplete Worksheet...

Problems with incomplete worksheet.

I have saved a .mw worksheet, which i cannot open in Maple, and i get an error code:

I have attached a link, where a user is helped with the same problem, but i cannot understand the solution there has been given:

https://www.mapleprimes.com/questions/125503-Incomplete-Worksheet

I have attached the worksheets, and would be so gratefull for any help:

Best regards

Henrik Jorgensen

## Ppossible Issue with Seq...

I am trying to work through an example in a textbook, but its a few years old and uses maple 2015. I am currently using the 2018 edition of maple. The code is an example of how to generate the points on an elliptic curve given a specific input.
Here is the example code from the textbook:

epoints := proc(ec, x, ub, p)
local ecurve, z, pct, k, i;
pct := 0;
for k from 0 to p-1 while pct <= ub do
z := subs(x=k, ec) mod p;
if z = 0 then
pct := pct+1;
ecurve[pct] := [k,z];
fi:
if z &^ ((p-1)/2) mod p = 1 then
z := z &^ ((p+1)/4) mod p;
ecurve[pct+1] := [k,z];
ecurve[pct+2] := [k, -z mod p];
pct := pct+2;
fi:
od:
if pct > ub then
pct := ub:
fi:
seq(ecurve[i], i=1..pct):
end:

Here is my code, written to work with Maple 2018:

ecpoints := proc (ec, x, ub, p) local ecurve, z, pct, k, i;
pct := 0; for k from 0 to p-1 while pct <= ub
do z := `mod`(subs(x = k, ec), p);
if z = 0 then pct := pct+1;
ecurve[pct] := [k, z] end if;
if `mod`(z^((1/2)*p-1/2), p) = 1 then
z := `mod`(z^((1/4)*p+1/4), p) = 1;
ecurve[pct+1] := [k, z];
ecurve[pct+2] := [k, `mod`(-z, p)];
pct := pct+2 end if
end do;
if ub < pct then pct := ub end if;

seq(ecurve[i], i = 1 .. pct)
end proc

The problem is with the output. The output should be [0, 5], [0, 14], [2, 4], [2, 15], [3, 6], [3, 13], [4, 6], [4, 13], [6, 0], [10, 16], [10, 3], [12, 6], [12, 13], [14, 16], [14, 3], [18, 17], [18, 2].
What I get is [0, 5 = 1], [0, 14 = 18], [2, 4 = 1], [2, 15 = 18], [3, 6 = 1], [3, 13 = 18], [4, 6 = 1], [4, 13 = 18], [6, 0], [10, 16 = 1], [10, 3 = 18], [12, 6 = 1], [12, 13 = 18], [14, 16 = 1], [14, 3 = 18], [18, 17 = 1], [18, 2 = 18].
Any hints on what I could be doing wrong here or what is going on?

## How to translate "blank pattern" to maple? ...

Hello

Moving from Mathematica to Maple and back these couple of days is driving me insane.  I get stuck trying to translate very simple things for not knowing each command belongs to each software.  Therefore I do apologize for another silly question.

Given the list of indexed variables

varA := [A[1, 0], A[1, 1], A[1, 2], A[1, 3], A[1, 4], A[1, 5], A[1, 6], A[1, 7], A[1, 8], A[1, 9], A[2, 0], A[2, 1], A[2, 2], A[2, 3], A[2, 4], A[2, 5], A[2, 6], A[2, 7], A[2, 8], A[2, 9], A[3, 0], A[3, 1], A[3, 2], A[3, 3], A[3, 4], A[3, 5], A[3, 6], A[3, 7], A[3, 8], A[3, 9]]

how to apply the following substitution

varA/. {Subscript[A, m_, 2] -> Subscript[B, m, 3],
Subscript[A, m_, 3] -> Subscript[B, m, 2],
Subscript[A, m_, 5] -> Subscript[B, m, 6],
Subscript[A, m_, 6] -> Subscript[B, m, 5],
Subscript[A, m_, 7] -> Subscript[B, m, 9],
Subscript[A, m_, 9] -> Subscript[B, m, 7]}

After trying a couple of commands such as map, subs, etc. I decide to try fromMma but no avail.

Many thanks for the patience and help.

Ed

## How to solve system of PDEs?...

I want to solve the following system of PDEs with Maple:

In fact, I want to determine q1,n1,p1,nn1,qn1,pn1 as a functions of pphi1 (assume  ne1(X,T)=(alpha/(2))*pphi1(X,T))

(mu, nu, beta, lambda, TE , alpha and TT are constant, but q1,n1,p1,nn1,qn1,pn1 depend on (X,T))

How do I do that?

> diff(q1(X, T), X)-lambda*(diff(n1(X, T), X)) = 0;

diff(pphi1(X, T), X)+TE*(diff(p1(X, T), X))-lambda*(diff(q1(X, T), X)) = 0;

-lambda*(diff(p1(X, T), X))+3*(diff(q1(X, T), X)) = 0;

-lambda*(diff(nn1(X, T), X))+diff(qn1(X, T), X) = 0;

-lambda*(diff(qn1(X, T), X))+beta*TT*(diff(pn1(X, T), X))-beta*(diff(pphi1(X, T), X)) = 0;

-lambda*(diff(pn1(X, T), X))+3*(diff(qn1(X, T), X)) = 0;

-mu*ne1(X, T)-nu*nn1(X, T)+n1(X, T) = 0;

## Ordinary differential equation with singularity...

Dear All,

I am trying to solve the following differential equation, which is a kind of Spherical Harmonics. Can anyone please help me out how to solve this?

((D@@2)(y))(r)+(D(y))(r)/r-sin(y(r))*cos(y(r))/r^2+sin(y(r))^2/r-sin(y(r))-sin(2*y(r)) = 0

Thanks

## How can I improve a plot in Maple?...

Hello every one:

I am trying to plat the graph of a function (which has been defined in my code). I use the plat 3D operator but it doesn't give me the correct plot . I even increase the digites and numpoints but appearently it gave me less precise plot .

The problem of plots is as follows :

First I defined the function V and  asking maple to compute the values of V at some random points, spacially at (0,0) , (0,2*Pi) and (2*Pi,0) . It gave me 0 which means Maple computes the values correctly because it can be mathematically proved  that this function has the value 0 on all the board of a triangle with vertices (0,0) , (0,2*Pi) and (2*Pi,0) .

As you can see in my code maple doesn't show the correct value (0)  for the boundary points even at (0,0) !

I don't know how shoud I fix this problem.You can find my code in attached .Thanks in advanced for your help. Maple_question.mw

## why same integrand gives different output from int...

Could some Maple expert please explain this strange behavior of int? Using Maple 2020 on windows 10

Same integrand. But in one case exp(arcsin(x)) and in another exp(1)^arcsin(x). Why one worked and not the other?

Here is the code

restart;
integrand1 := (x^3*exp(arcsin(x)))/sqrt(1 - x^2);
integrand2 := (x^3*exp(1)^arcsin(x))/sqrt(1 - x^2);
simplify(integrand1-integrand2);
int(integrand1,x);
int(integrand2,x)

## Combining square roots not happening even when ass...

I have a simple little physics scenario that I'd like to nicely pretty print showing the relationships between KE = elastic PE to find velocity when the object returns back to x=0.

This resolves to:

It would be nice to have all the individual terms reduce like how this works in Mathematica:

FullSimplify[Solve[1/2*m*v^2 == 1/2*F*x, v], {F > 0, x > 0, m > 1}]

Any tips on how to get all the square roots to reduce?