## Solve Simple Equation...

Hi all,

Is there anyone who could help me with this error? I am sure there is at least one solution for the equation.

Thanks

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/EQ.mw .

## RootOf expressions...

suppose one has a solution to a system of equations that returns results as RootOf(X) expressions. I would like to know if there is a procedure for extracting the "X" from the RootOf for the purpose of further algebraic analysis.

## two problem about RootOf and Float(undefined) in ...

hello.

i have two problem in maple file, that is attached..

one of them is RootOf...note that i suppose that [varepsilon := -2.3650203724313] for i can going on following calculation

and second is  Float(undefined) in calculation integral

thanks

(m=1_n=6)2.mw

## How do I get a better solution?...

Here is my code in Maple.

#Solve the initial-value problem using the technique of question 2. Find the implicit solution.
eqn3:=(exp(x)+y)*dx+(2+x+y*exp(y))*dy=0;
(exp(x) + y) dx + (2 + x + y exp(y)) dy = 0
#subject to y(0)=1.
M:=exp(x)+y; N:=2+x+y*exp(y);
exp(x) + y
2 + x + y exp(y)
int(M, x); int(N,y);
exp(x) + y x
y x + 2 y + y exp(y) - exp(y)
implicitsoln1 := exp(x)+y*x+2*y+y*exp(y)-exp(y)=C;
exp(x) + y x + 2 y + y exp(y) - exp(y) = C
y1 := solve(implicitsoln1,y);
RootOf(-exp(_Z) _Z - _Z x + C + exp(_Z) - 2 _Z - exp(x))
C:=subs({x=0,y=1},lhs(implicitsoln1));
exp(0) + 2
y1;

How do I get it to to not have "root of" and give me a more specific solution.

## Is `evala/toprof` command in new Maple versions?...

Does `evala/toprof` still exist in newer Maple versions, or is there an equivalent?

## Problem with RootOf...

With the following equation

eqn:=y=1/2+(1/2)*erf((1/2)*sqrt(2)*(x-mu)/sigma)-exp(-lambda*(x-mu)+(1/2)*lambda^2*sigma^2+ln(1/2-(1/2)*erf((1/2)*sqrt(2)*(lambda^2*sigma^2-lambda*(x-mu))/(lambda*sigma))));

and with

x:=solve(eqn,x) assuming sigma > 0, lambda > 0;

I got the following solution

x := -(1/2)*(-lambda^2*sigma^2-2*lambda*mu+2*RootOf(-exp(_Z)*erf((1/4)*sqrt(2)*(lambda^2*sigma^2+2*_Z)/(lambda*sigma))+exp(_Z)+erf((1/4)*sqrt(2)*(-lambda^2*sigma^2+2*_Z)/(lambda*sigma))+2*y-1))/lambda;

In order to get rid of RootOf I gave the command:

allvalues(%);

However, RootOf did not disappear. How should I proceed?

## Simplification of RootOf...

hi...how i can gain result for solve three equations,in which term '' Root of'' dont appear?

thanks

 (1)

 (2)

 (3)

 (4)

 (5)

## Problem with dsolve...

Dear all,

I am trying to solve the following system of equations by using dsolve, but I get the error:  error, (in RootOf) expression independent of, _Z, could you please help me to solve it. Thank you.

restart;
Digits := 20;
with(plots);
Nr := .1; Nb := .3; Nt := .1; Rb := 0; Lb := 1; Le := 10; Pe := 1; ss := .2; aa := .1; bb := .2; cc := .3; nn := 1.5;
Eq1 := nn.(diff(f(eta), eta))^(nn-1).(diff(f(eta), `\$`(eta, 2)))-(nn+1)/(2.*nn+1).eta.(diff(theta(eta), eta)-Nr.(diff(h(eta), eta))-Rb.(diff(g(eta), eta))) = 0;
Eq2 := diff(theta(eta), `\$`(eta, 2))+nn/(2.*nn+1).f(eta).(diff(theta(eta), eta))+Nb.(diff(theta(eta), eta)).(diff(h(eta), eta))+Nt.((diff(theta(eta), eta))^2) = 0;
Eq3 := diff(h(eta), `\$`(eta, 2))+nn/(2.*nn+1).Le.f(eta).(diff(h(eta), eta))+Nt/Nb.(diff(theta(eta), `\$`(eta, 2))) = 0;
Eq4 := diff(g(eta), `\$`(eta, 2))+nn/(2.*nn+1).Lb.f(eta).(diff(g(eta), eta))-Pe.((diff(g(eta), eta)).(diff(h(eta), eta))+(diff(h(eta), `\$`(eta, 2))).g(eta)) = 0;
etainf := 10;
bcs := f(0) = ss/Le.(D(h))(0), theta(0) = lambda+aa.(D(theta))(0), h(0) = lambda+bb.(D(h))(0), g(0) = lambda+cc.(D(g))(0), (D(f))(etainf) = 0, theta(etainf) = 0, h(etainf) = 0, g(etainf) = 0;
dsys := {Eq1, Eq2, Eq3, Eq4, bcs};
dsol := dsolve(dsys, numeric, continuation = lambda, output = procedurelist);
Error, (in RootOf) expression independent of, _Z

## Problem with symbolical solution...

Hi,

I have been trying to solve the following equation with respect to y, but I have not been successful. In fact, I always get answer RootOf(...). I should mention that all variables and parameters are real non-negative. I have also tested with "assume", but it did not help. Any suggestion would be appreciated.

 (1)

 (2)

 (3)

Thanks.

## How to get rid of RootOf?...

hi.please see attached file below and help me for gain real or complex answer

with out show answer in root of manner

thanksroot_of....mw

## Trouble with RootOf in set...

Hello everyone! I got some trouble in process a list. Hope you can help:

Assume i got a list like this:

{{k = k, l = RootOf(_Z^2+_Z*k+k^2-1), o = -k-RootOf(_Z^2+_Z*k+k^2-1)}, {k = k, l = RootOf(_Z^2+_Z*k+k^2+1), o = -k-RootOf(_Z^2+_Z*k+k^2+1)}, {k = 0, l = 1, o = -1}, {k = 0, l = -1, o = 1}, {k = 1, l = 0, o = -1}, {k = 1, l = -1, o = 0}, {k = -1, l = 0, o = 1}, {k = -1, l = 1, o = 0}, {k = RootOf(_Z^2+1), l = 0, o = -RootOf(_Z^2+1)}, {k = RootOf(_Z^2+1), l = -RootOf(_Z^2+1), o = 0}}

Now all i want is remove Complex and RootOf from this list, how can i do that?

## Obtaining the splitting field...

I am trying to obtain the splitting field of New_polyq. evala@AFactor did not complete. Applying splitting sequentially produced independent extensions from the first 2 (3?) factors. evala@Indep did not complete for the union of all 4 extensions.

What libraries would handle this better?

restart; _EnvExplicit:=false;interface(labelwidth=200);
Rho_polys:=rho[3,1]^3-2, rho[3,2]^2+rho[3,2]*rho[3,1]+rho[3,1]^2, 2*rho[6,1]^3+rho[6,1]^6-2, rho[12,1]^2+rho[6,1]^2-1, 2*rho[12,2]^2-rho[6,1]^2*rho[3,2]*rho[3,1]^2-2*rho[6,1]^2-2;
New_poly:=1/16*(-rho[6,1]^4*rho[3,2]*rho[3,1]-2-rho[3,1]^2*rho[6,1]^4-2*rho[6,1]*rho[3,2]*rho[3,1]-2*rho[3,1]^2*rho[6,1]+2*lambda^2)*(rho[6,1]^4*rho[3,2]*rho[3,1]+2*rho[6,1]*rho[3,2]*rho[3,1]-2+2*lambda^2)*(-2+2*rho[3,1]^2*rho[6,1]+rho[3,1]^2*rho[6,1]^4+2*lambda^2)*(-2+rho[6,1]^2*rho[3,2]*rho[3,1]^2+2*lambda^2);
sol:=solve({Rho_polys});
alias(op(sol));
New_polyq:=subs(sol,New_poly);

## Solving an equation...

Hi everyone,

I'm trying to solve the following eqauation but Maple gives me the answer (( RootOf(mexp(-_Z*(m-1))*d^2-theta+_Z*theta-theta*c*t__kj) ))

The equation is:

solve(mexp(-(m-1)*t__ij)*d^2-theta+theta*t__ij-theta*(sum(t__kj, k = 1 .. c))-m*eta*(diff((1-1/exp(t))^m, t)) = 0, t__ij);

What is the meaning rootOF? Is there any explicit solution to that equation??

## Solving a combined system of differential and part...

Dear Maple enthusiasts,

I am unable to find a working method to solve a system of 8 equations, of which 4 are differential equations. The system contains 8 unknown variables and the goal is to find an expression for each of these variables as a function of the time t. I have attached the code of my project at the bottom of this message.

I have tried the following:

1. Using solve/dsolve to solve all 8 equations at once. This results in Maple eating up all of my memory and never finishing its calculations.
2. First using solve to solve the 4 non-differential equations so that I get 4 out of 8 variables as a function of the 4 remaining variables. This results in an expression containing RootOf() for each of the 4 veriables I'm solving for, which prevents me from using these expressions in the 4 remaining differential equations.
3. First using dsolve to solve the differential equations, which gives once again an expression for 4 variables as a function of the 4 remaining variables. I then use solve to solve the 4 remaining equations with the new found expressions. This results in an extremely long solution for each of the variables.

The code below contains the 3rd option I tried.

Any help or suggestions would be greatly appreciated. I have been scratching my head so much that I'm getting bald and whatever I search for on google or in the Maple help, I can't find a good reference to a system of differential equations together with other equations.

 > restart:

PARK - Mixed control

Input parameters

Projected interface area (m²)

 > A_int:=0.025^2*Pi:

Temperature of the process (K)

 > T_proc:=1873:

Densities (kg/m³)

 > Rho_m:=7000: metal
 > Rho_s:=2850: slag

Masses (kg)

 > W_m:=0.5: metal
 > W_s:=0.075: slag

Mass transfer coefficients (m/s)

 > m_Al:=3*10^(-4):
 > m_Si:=3*10^(-4):
 > m_SiO2:=3*10^(-5):
 > m_Al2O3:=3*10^(-5):

Weight percentages in bulk at t=0 (%)

 > Pct_Al_b0:=0.3:
 > Pct_Si_b0:=0:
 > Pct_SiO2_b0:=5:
 > Pct_Al2O3_b0:=50:

Weight percentages in bulk at equilibrium (%)

 > Pct_Al_beq:=0.132:
 > Pct_Si_beq:=0.131:
 > Pct_SiO2_beq:=3.13:
 > Pct_Al2O3_beq:=52.12:

Weight percentages at the interface (%)

Constants

Atomic weights (g/mol)

 > AW_Al:=26.9815385:
 > AW_Si:=28.085:
 > AW_O:=15.999:
 > AW_Mg:=24.305:
 > AW_Ca:=40.078:

Molecular weights (g/mol)

 > MW_SiO2:=AW_Si+2*AW_O:
 > MW_Al2O3:=2*AW_Al+3*AW_O:
 > MW_MgO:=AW_Mg+AW_O:
 > MW_CaO:=AW_Ca+AW_O:

Gas constant (m³*Pa/[K*mol])

 > R_cst:=8.3144621:

Variables

 > with(PDEtools): declare((Pct_Al_b(t),Pct_Al_i(t),Pct_Si_b(t),Pct_Si_i(t),Pct_SiO2_b(t),Pct_SiO2_i(t),Pct_Al2O3_b(t),Pct_Al2O3_i(t))(t),prime=t):

Equations

4 rate equations

 > Rate_eq1:=diff(Pct_Al_b(t),t)=-A_int*Rho_m*m_Al/W_m*(Pct_Al_b(t)-Pct_Al_i(t));

 > Rate_eq2:=diff(Pct_Si_b(t),t)=-A_int*Rho_m*m_Si/W_m*(Pct_Si_b(t)-Pct_Si_i(t));

 > Rate_eq3:=diff(Pct_SiO2_b(t),t)=-A_int*Rho_s*m_SiO2/W_s*(Pct_SiO2_b(t)-Pct_SiO2_i(t));

 > Rate_eq4:=diff(Pct_Al2O3_b(t),t)=-A_int*Rho_s*m_Al2O3/W_s*(Pct_Al2O3_b(t)-Pct_Al2O3_i(t));

3 mass balance equations

 > Mass_eq1:=0=(Pct_Al_b(t)-Pct_Al_i(t))+4*AW_Al/(3*AW_Si)*(Pct_Si_b(t)-Pct_Si_i(t));

 > Mass_eq2:=0=(Pct_Al_b(t)-Pct_Al_i(t))+4*Rho_s*m_SiO2*W_m*AW_Al/(3*Rho_m*m_Al*W_s*MW_SiO2)*(Pct_SiO2_b(t)-Pct_SiO2_i(t));

 > Mass_eq3:=0=(Pct_Al_b(t)-Pct_Al_i(t))+2*Rho_s*m_Al2O3*W_m*AW_Al/(Rho_m*m_Al*W_s*MW_Al2O3)*(Pct_Al2O3_b(t)-Pct_Al2O3_i(t));

1 local equilibrium equation

Gibbs free energy of the reaction when all of the reactants and products are in their standard states (J/mol). Al and Si activities are in 1 wt pct standard state in liquid Fe. SiO2 and Al2O3 activities are in respect to pure solid state.

 > delta_G0:=-720680+133*T_proc:

Expression of mole fractions as a function of weight percentages (whereby MgO is not taken into account, but instead replaced by CaO ?)

 > x_Al2O3_i(t):=(Pct_Al2O3_i(t)/MW_Al2O3)/(Pct_Al2O3_i(t)/MW_Al2O3 + Pct_SiO2_i(t)/MW_SiO2 + (100-Pct_SiO2_i(t)-Pct_Al2O3_i(t))/MW_CaO); x_SiO2_i(t):=(Pct_SiO2_i(t)/MW_SiO2)/(Pct_Al2O3_i(t)/MW_Al2O3 + Pct_SiO2_i(t)/MW_SiO2 + (100-Pct_SiO2_i(t)-Pct_Al2O3_i(t))/MW_CaO);

Activity coefficients

 > Gamma_Al_Hry:=1: because very low percentage present  during the process (~Henry's law)
 > Gamma_Si_Hry:=1: because very low percentage present  during the process (~Henry's law)
 > Gamma_Al2O3_Ra:=1: temporary value!
 > Gamma_SiO2_Ra:=10^(-4.85279678314968+0.457486603678622*Pct_SiO2_b(t)); very small activity coefficient? plot(10^(-4.85279678314968+0.457486603678622*Pct_SiO2_b),Pct_SiO2_b=3..7);

Activities of components

 > a_Al_Hry:=Gamma_Al_Hry*Pct_Al_i(t); a_Si_Hry:=Gamma_Si_Hry*Pct_Si_i(t); a_Al2O3_Ra:=Gamma_Al2O3_Ra*x_Al2O3_i(t); a_SiO2_Ra:=Gamma_SiO2_Ra*x_SiO2_i(t);

Expressions for the equilibrium constant K

 > K_cst:=exp(-delta_G0/(R_cst*T_proc));
 > Equil_eq:=0=K_cst*a_Al_Hry^4*a_SiO2_Ra^3-a_Si_Hry^3*a_Al2O3_Ra^2;

Output

 > with(ListTools): dsys:=Rate_eq1,Rate_eq2,Rate_eq3,Rate_eq4: dvars:={Pct_Al2O3_b(t),Pct_SiO2_b(t),Pct_Al_b(t),Pct_Si_b(t)}: dconds:=Pct_Al2O3_b(0)=Pct_Al2O3_b0,Pct_SiO2_b(0)=Pct_SiO2_b0,Pct_Si_b(0)=Pct_Si_b0,Pct_Al_b(0)=Pct_Al_b0: dsol:=dsolve({dsys,dconds},dvars):
 > Pct_Al2O3_b(t):=rhs(select(has,dsol,Pct_Al2O3_b)[1]); Pct_Al_b(t):=rhs(select(has,dsol,Pct_Al_b)[1]); Pct_SiO2_b(t):=rhs(select(has,dsol,Pct_SiO2_b)[1]); Pct_Si_b(t):=rhs(select(has,dsol,Pct_Si_b)[1]);
 > sys:={Equil_eq,Mass_eq1,Mass_eq2,Mass_eq3}: vars:={Pct_Al2O3_i(t),Pct_SiO2_i(t),Pct_Al_i(t),Pct_Si_i(t)}: sol:=solve(sys,vars);

,

## Why does allvalues not eliminate all RootOf's ?...

Hi guys,

im trying to solve the linear equation system:

Then, assigning the solutions:

Then, eliminating the RootOf's for variable a:

Unfortunately, a_explicit still contains RootOf's. How can I avoid this?

Thanks,

Martin

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