**3.106 equation-solving questions.**

I have a method that finds the location of the minima of a function (derived in this question).
...

I'm new to Mathematica and I'm trying to solve a partial differential equation involving 1D Fick's second law with a reaction term that's a function of the concentration (C)
$$\ ∂C/∂t=D (∂^2 C)/(∂x^2 ...

Recently, I am doing a course project, and the professor forces us to use Mathematica; however, I am new to Mathematica, and here are my problems.
Setup
I am required to, eventually, numerically ...

I will do my best to describe the simplest version of my problem as clearly as I can. Please bear with me:
We have a,b and c which are functions of x and y, and their t-evolution is given by coupled ...

Let be $ABCD$ is a tetrahedron, knowing that $ABC$ is an equilateral triangle $AB=a$, $AD=d$, $BD=e$, $CD=f$. I want to find the $a$, $d$, $e$, $f$ when the angle of two vectors $AB$ and $CD$ equal to ...

I was using the pdetoode function that @xzczd made:
Dynamic Euler–Bernoulli beam equation
But it only works for functions with 2 variables, I was wondering if it ...

I am a great fan of Mathematica. Unfortunately, due to some specific tasks I had to move to Maple. I think it's my lack of info that is not letting me do those tasks. That is why I am asking some ...

i want to solve the nolinear equations and $\phi1\in(0,\frac{\pi}{2})$ and $\phi2\in(0,\frac{\pi}{2})$ and $\phi1<\phi2$
I calculated the maximum and minimum on the left of the equal sign, and ...

The following is a curiosity I just observed. Consider the following Reduce command:
...

I am trying to reduce a bunch of inequalities using the Reduce command in Mathematica. But the output is very convoluted and I am wondering if there's a way to systematically organize it so that I can ...

Suppose that I want to take a solution of an equation, for examplea=Solve[x+3==0,x]and use it as a number, for example to evaluate another expression such as:<...

The following is example of back substituting FindRoot solution into initial values using a table.
...

How can I make this work? Sorry I couldn't write it from my phone so I uploaded a photo of it.

how to solve u dC/dx=d(Kz d/dz)/dz in mathematica
br
S.

I'm working on differential equations and I first used a potential without Piecewise. But given that I wanted to constrain the values between 0 and 1, I started to use Piecewise in the potential, ...

I was using Mathematica 11.1 to solve a PDE system numerically, but it told me that the system is overdetermined. So I tried a much simpler one. Here is the input.
...

Bug introduced in 8.0.4 or earlier, persisting in part through 11.3.
I was willing to solve this nonlinear PDE:
...

I'm trying to solve nonlinear equations using Newton-type methods with very high accuracy using Mathematica. I found many research papers in which the numerical results are calculated with very high ...

In this equation, the $T_0,p,l_1,\rho,C_{DN},d$ are all known and constant. I want to get every $v$, every $x_1$. I can get an $x_2$, and finally get the $x_2-x)_1$ varies as $v$.
The $v$ is from $0-...

I am running a code that finds the minima of a 2D function f in an ever larger window. I am basing my minimsation plot on this method, which basically used ...

In my notebook, I obtain an expression that I can't figure out how to reduce to it's simplest form. I've recreated it below to show what I am trying to simplify.
...

Consider the following function:f[θ_] =
Integrate[1/(Cot[θ]^2 - Sin[θ]^2)^(1/2), θ];Now, I want to determine the value of $\theta$ for which say $f(θ)=1$. I ...

I have a system of equations with a single parameter Ee that I would like to vary from 0 to 1 with step sizes of 0.01. I have been able to get solutions with this format by manually changing Ee (...

I have received an expression from a Reduce:
...

How can we find all inverses of a multivalued function using Mathematica?
For example, if we try to find the inverse of $x^2$, Mathematica will say something like this:
...

A few months ago, I thought of a marvelous proof that $a^3+b^3=2c^3$ has no nontrivial integer solutions in $\mathbb{N}$, but the margin of my cocktail napkin was too small to contain it. Now I've ...

I have a $4$-dimensional nonlinear system of second order PDEs with periodic boundary conditions. Let $y(t,x)=(y_1(t,x),...,y_4(t,x))$ with $t \in \mathbb{R}$ and $x \in [0,1]$ then the system is
$$\...

Is it possible to remove a term which includes a defined variable from an equation?
my equation is something like:
...

Bug introduced in 8.0.4 or earlier, persisting through 11.3DSolve quickly returns solutions to the following PDE (which is the homogeneous portion of the PDE in ...

I am at a loss how to transform the following function:
$\qquad \Bigg[\Bigg(\omega^{2}-\alpha+\beta*z^{4}\Bigg)^{2}+ (\delta*\omega)^{2}\Bigg]*z^{2} = \gamma$
into an explicit dependance of $z$ on $\...

I have the following equation;
...

I am a new user in Wolfram language.
Please, I am trying to calculate accurate solutions $R$ of an algébric equation which contains the Dawson function. The equation is:
$$1+\frac{\theta }{k^2}+\...

M = 1/10;
sol = NSolve[{n == 1/(2 M) + e/Tan[2 e], e == 1/(2 M)*Sqrt[Exp[4 n] - (1 -
2*M*n)^2], 1/10 < e < 6, -1 < n < 1}, {e, n}];It gives ...

I have looked at a few places in order to find an answer to my question - specifically, I have looked at this old Mathematica documentation page, at the Preconditioner option for NDSolve, as explained ...

I'm trying to solve the following equation, but it runs for three days and does not converge to a solution. Do you have any suggestion on how to solve it?
...

That is,
I want to solve these equations below:
1-(Sin[\[Delta]] Cos[\[Lambda]] Sin[2 \[Phi]] +
Sin[2 \[Delta]] Sin[\[Lambda]] Sin[\[Phi]]^2)==02
...

Let $B_R$ be a ball of radius $R>0$ centered at the origin in $\mathbb{R}^2$.
Consider the PDE $u_t + \nabla \cdot (u^2 \nabla \Delta u) = 0$, in $ (0,T)\times B_R,$ with boundary conditions $u =\...

Consider the following two test-cases:Reduce[{a^3 + 1 == 0, b^15 - b^3 + 1 == 0}, {a, b}, Backsubstitution -> True]Gives an output roughly:
...

I want to solve the nonlinear PDE for the anisotropic fluid flow:
$-\rho*\partial{v_i}/\partial{t} + (C_{ijkl}v_{k,l})_{,j}-p_{,j} = 0$
(The nonlinear term $-v_jv_{i,j}$ will be added later)
Here ...

How can I find the points of intersection of cosh(x) and sec(x)?
Plotting the two, I can see that it has a root around 4.7, but then I can't tell where the next root is.
But when I use ...

I'm trying to model the following system of $n$ nonlinear differential equations:
$$
\dot{P}_i(t) = \sum_{1 \, \leq \, j \, < \, i} R(p_{ji}) - A(p_{ji}) + \sum_{i \, < \, j \, \leq \, N} A(p_{...

I have a square matrix ${\bf A}$ defined over the field $\mathbb Z_2$ and I want to find its order such that ${\bf A}^m=1$. I tried using
...

I kindly ask if someone could help me solve this problem:
I have solved a differential equation by varying a parameter that I called by $\alpha$ as follows:
...

I would like to find the value n satisfying following equation . How can I do it in Mathematica?
15411 == 123*Fibonacci[n] + 31*Fibonacci[n + 1]

In the following lines of code, we are trying to compute the L-moment estimates of the parameters of the Kumaraswamy distribution. But as you notice, neither <...

$h - (2A) / t^3 - K/t^2 + b*C*e^{b*t} =\\ \, \, 3^{1/2}*B + 3*p*(A/t^2 + E/t + h*t + C*e^{b*t})- \\ \,\,3^{1/2}*(g + 1)*(A/t^2 + E/t + h*t + C*e^{b*t})^{3/2}$
How can I find the values of the ...

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