Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

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Solving a nonlinear equation involving convolution

I consider the following functional : $\psi(u,v)= -u(1-v)(1-\alpha k * v) + \epsilon v (\alpha k * v)$, where $k(x)$ is a smooth kernel with $\int |k| = 1$ and $\int k_+ = \alpha \in ]0,1[$, $u(x), ...
1
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2answers
102 views

Plotting the solution of a cubic equation against a coefficient in the equation

I have to plot the solution of the following equation against the coefficient $L$. Since it's a cubic equation, I'd like to filter out the real solution first and plot that then. The equation is $L ...
1
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1answer
80 views

Is it possible to solve a certain set of nonlinear equations in Mathematica?

I read this question in a Chinese forum last year. At the end of the discussion, they provide a solution of the equations from a C++ program. Unfortunately, they did not get the right answer. ...
0
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1answer
88 views

NDSolve issue with initial and boundary conditions

While solving the heat equation in one spatial variable $u_t = u_{xx} $ (x goes from 0 to L) with the initial temperature distribution $T_0 \frac{x(L-x)}{L^2}$ , and with neumann boundary conditions ...
2
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1answer
56 views

Plot directional field with a initial vlue

I do not have enough reputation to comment on other questions, hence I have to ask my own one I want to solve the following nonlinear first order ODE, $$(1 + x) (0.5 y[x]^{-0.5} (x - y[x])^{0.5} - ...
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0answers
42 views

Finding common roots to several functions

I am trying to solve the following problem. Given $a\in\mathbb R^n$, $u\in\mathbb{R}^n$, $m\in\mathbb{N}^\star$, Find the/some common roots $(t_1,...,t_m)$ of the $\frac{m(m-1)}{2}$ ...
2
votes
2answers
96 views

A peculiar behavior of NSolve[]

NSolve[Power[x + 1, x + 1] - Power[x, x + 2] == 0, x, Reals] returns: {{x -> 3.14104}} Great. However, ...
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1answer
56 views

Symbolically solve system of equations involving matrix

I need to solve the following system of equations symbolically for a_i, b_i, and c_i: ...
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0answers
84 views

Can Mathematica Find Closed-Form Solution this Equation

I have tries to solve an equation by using Solve[] to find pl as a function of other variables. However, it generates an Error! Can anyone help? ...
6
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0answers
66 views

Strange result of Reduce and ForAll

In the question Can Mathematica tell me if a polynomial has all real roots?, quite a few of interesting answers were given. I wanted to add another one, using quantors, and observed some strange ...
8
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5answers
712 views
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1answer
56 views

Question about the third argument of Solve [duplicate]

I'm learning about derivatives. This is my code: ...
2
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2answers
103 views

Study the possible coincidences of the three clock hands hour, minute, and second

Inspired by the very nice problem solutions of the problem of coinciding clock hands, I'd like to extend the question including a "second" hand. While it is obvious that all three hand can coincide ...
3
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2answers
313 views

How to solve numerically an equation which contains numerical intergration?

F1[x_] := NIntegrate[E^Sin[y x], {y, 0, 1}] F2[x_] := Log[x] NSolve[F1[x] == F2[x], x] I want to solve the equation, but Mathematica don't solve it. ...
1
vote
1answer
94 views

Solving a complex logarithmic equation

I am trying to solve the following equation for $x$, with integer $n$. (1 - ((-1 + x)^E x^(1 - x) Log[x]^-E)^(1/(-1 + E)))/(-1 + x) == n
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0answers
62 views
19
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4answers
850 views

Hightlight all the self-intersections of a Lissajous figure

This graph–also known as a Lissajous figure–contains so many self-intersections.How can I highlight them? ...
0
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1answer
40 views

Solve and NSolve hitting iteration limit for simple system [closed]

I'm am trying to get Mathematica to determine the intersection of a line and a parabola, like so: Solve[{x + y == 6, x^2 == y}, {x, y}] But evaluating this gives ...
0
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1answer
52 views

Question about a catalytic equality?

I have a question on math.SE that explains how I came up with these equations. ...
2
votes
1answer
74 views

Reduce / Solve cannot solve simple equation

Why does Reduce[{a^b*c^b == c, 0 < b < 1, a > 0, c > 0}, c, Reals] give ...
2
votes
3answers
139 views

Find roots of a peak to calculate its width at 10% peak height

I have numeric data points (x,y) values from a peak. I constructed a interpolation to get an interpolating function. Interpolation[data] What I want to do is the ...
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1answer
39 views
0
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1answer
46 views

Recursion depth and solving equations using Solve

I am trying to solve an equation: ...
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2answers
213 views

How to Fit experimental data with 4D ParametricNDSolve?

Let me first explain the background problem. I'm trying to solve a problem with a projectile motion in 4D such that the position vector is: $\boldsymbol{r}(t)=\boldsymbol{r}[x(t),y(t),z(t)]$ I have ...
0
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1answer
56 views

Solving a vector equation [duplicate]

I want a simple and intuitive way of solving for $t$ given that $\mathbf{i},\, \mathbf{j},\, \mathbf{k}$ are the unit vectors in $\mathbf{R}^3$. $$ 5 = (2 \mathbf{i} - 3 \mathbf{k} + (\mathbf{i} - ...
4
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5answers
241 views

On finding all the positive integral solutions of $x^2+y^2=z^2+1$

I am a new to Mathematica. My goal is to find many (if not all) positive integer solutions to the equation: $x^2+y^2=z^2+1$ using Mathematica. However the problem is that I can only find a ...
0
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0answers
62 views

How can I be sure Solve failed because there was no solution to be found?

Is there a way I can be sure that the reason Mathematica can't find an answer is because there isn't one, rather than because I made a mistake with the code? The system is as follows. ...
3
votes
2answers
183 views

Creepy numerical artefacts of a closed-form solution

I'm wishing you a nice day and here is my problem: I tried to obtain relation between chemical potential and temperature in a semiconductor and I arrived at this equation: $$ 2 e^{-\Delta/kT} \left( ...
2
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1answer
78 views

Can't NSolve system of exponential and linear equations in several variables

At the moment I am stuck with the following code, when specified to use root , quadratic or log utility functions all it fine, only exponentials like: $\small \left\{-e^{-c_{0,1}}-0.25 ...
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0answers
49 views

Solve equations for derivatives

I want to solve some equations in General Relativity numerically with the Runge-Kutta method. Therefore, I need to solve for example $r^{''} \left(\tau\right) + t\left(\tau\right) + a = 3 $, where $ ...
0
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0answers
57 views

Computing the coefficients for Gaussian integral

I wrote a small script to find the Gaussian integral points and weights: ...
0
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0answers
97 views

NSolve and Loop - getting error that does not occur with single instance

I am having difficulties getting this code to work. Code: ...
0
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0answers
59 views

Plot zero contour of a function of two variables

I have F[x_,y_] = f(x,y). I would like to solve (numerically) F[x,y] == 0 to give x as ...
1
vote
1answer
69 views

Computing a recurrence table backward

I am trying to understand how to compute a recursive equation backward say n = 10 to n = 1. I am trying to solve a PDE for which ...
1
vote
1answer
331 views

Usage of Piecewise/RSolve to solve an equation based on condition

I am trying to compute price of call option on a stock using the finite difference method. I have a VBA code for it, and I am trying to find out how I can use Mathematica memoization functions and ...
1
vote
1answer
87 views

Solve system of equations with implicit function [closed]

I am trying to solve a system of 3 (non-linear) equations with two variables $x,\ y$ and one unknown function $f(x,y)$ of these two variables. Also, the system includes the change of this function $f$ ...
1
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3answers
88 views

Getting a list of x coordinates of intersection points of two functions

I have two functions, f[x_] := 5 Sin[2 x] g[x_] := (5 x + 2)/(x + 2) I am trying to find the x coordinates that intersect ...
0
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0answers
39 views

Deciphering output messages using Solve

I'm trying to solve the following system. The error messages I'm getting suggest that there may not be a solution [my desired result], but I'm not sure if there could be something else going on. The ...
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0answers
45 views

How to speed up geometric Resolve query involving $\exists$ and $\forall$?

I would want to test connectedness of semialgebraic sets with naive code like this: ...
0
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0answers
42 views

RSolve with two variables

I want to find $a(m,n)$ with $~a(m,n)=\alpha * a(m-1,n) + \beta * a(m,n-1)$, where $\alpha$ and $\beta$ are constants. I expect an explicit $a(m,n)$ represented by $a(0,j),~j=1,2,\cdots,n$ and ...
0
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1answer
53 views

DSolve not outputting any result

I'm trying to solve a system of differential equations using DSolve, but I am not getting any output beyond a repetition of my input: ...
0
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1answer
88 views

Manipulate Solve

I have seen similar questions and answers but it did not help me. I would like to see effects of three constants in equations resulted from solve command. conditions are ...
1
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0answers
40 views

Tracking solutions over a Brillouin zone

Thanks to @bbgodfrey I have a function that finds the two solutions to a set of equations bounded by a hexagonal region (corresponding to the Brillouin zone). It takes the angle ...
6
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2answers
239 views

How to read complicated result from Reduce?

How can I read this Reduce output from Mathematica that I got from solving an inequality? I do not perfectly know when one case in this case analysis is over and ...
0
votes
1answer
148 views

RSolve with integrations

I want to solve this question with Mathematica. $$T_0(t)=c(t),\quad T_n(t)=a\int_0^t T_{n-1}(s)\, \mathrm{d}s+b(t).$$ Is it possible to solve $T_n(t)$ with ...
0
votes
1answer
122 views

Add assumptions to Solve command

I want Mathematica to solve the following by assuming the part within the Log function, which is ...
0
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0answers
71 views

Difficulty solving an equation involving a couple of different powers

I have this semi-complicated equation to which I want to find an analytical solution for $\epsilon$. The equation is a s following: $$a^2 (2 b k \epsilon \sqrt{1 - \epsilon^2/b^2} - 2 c k ...
0
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1answer
79 views

Equation solving problem [closed]

I have this code: ...
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0answers
25 views

Convert the output of solve into equality [duplicate]

I know this is has been asked before but seriously, none of the ones I checked helped because they referred to a single variable assignation. Apologies if this is a duplicate. I have many variables ...
0
votes
1answer
52 views