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

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0
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1answer
22 views

Hill function (equation) vs a gene

So im trying to make one equation equal another to solve for all physically realistic values of $X$. Hill function is: $$ F(X)=\frac{1}{1+(\frac{X}{K})^n} $$ and Gene Z equation is: $$ Z(X) = ...
0
votes
0answers
24 views

Generating vectors with restrictions on a lattice

Suppose we are given a certain adjacency matrix that contains the information for a given lattice. I want to generate a configuration of vectors that satisfy a restriction. Specifically, if I have ...
0
votes
0answers
51 views

NSolve can not handle a PolyGamma equation

I would like to solve the following equations numerically: ...
1
vote
1answer
33 views

Trying to find solution for system of ordinary differential Equations [on hold]

I've got 2 functions: A'[t] = (0.5/(1 + (B/k1)^n)) - 0.2*A B'[t] = (1/(1 + (A/k2)^n)) - 2*B with conditions of ...
0
votes
0answers
15 views

Recurrent equations [duplicate]

I want to make a relation to show the first 7 elements that don't have the number 7 in it. So far i know how to make it to show the first 7 elements with RecurrenceTable[{a[n + 1] == 7 a[n] + a[n], ...
5
votes
1answer
154 views

Solution to $y = x^x (1-x)^{(1-x)}$ for $x$ [on hold]

Does anyone have any insight to a symbolic Mathematica solution to this equation for $x$ in terms of y? Symbolic of any sort, just not numeric. $$y = x^x (1-x)^{(1-x)}$$
6
votes
2answers
171 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 ...
11
votes
3answers
450 views

How can we plot the complex roots of an equation?

If we'd like to display the $n$ roots of a polynomial on the complex plane as points, how can we do this? For example, if we have the equation $x^3 + x^2 + x + 1$, how can we plot the 3 roots as ...
0
votes
0answers
61 views

How to determine why Solve[] failed?

I don't know what to make of Solve[] failing on this: ...
21
votes
1answer
783 views

Bug in Solve (Mathematica 9)

The issue seems to be fixed as of Version 10.1. Just came across the strangest bug under both Mathematica 9.0.0 and 9.0.1. If one enters: ...
1
vote
1answer
88 views

Defining Solutions to FindRoot a functions of parameters-Part II

Here's a similar question as the the preceding question with the same title, but this time with vectors, which I need to use. I followed the suggestion in the answer the the previous question, but it ...
1
vote
1answer
72 views

How to speed or help Solve[] when it is stuck?

The code below generates a system of equations that I need to Solve[] for {c[5], c[6], c[7], c[8]} in terms of {c[1], c[2], c[3], c[4]}. ...
14
votes
2answers
430 views

Determining the default Method used in optimization and root-finding algorithms

Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, ...
0
votes
0answers
38 views

NSolve Duration for simultaneous equations solving

At the moment I am asking myself why mathematica gets to point of needing enormous amount of time to solve equations like these when one more "row" or "colum" or both was added in this equations ...
0
votes
0answers
75 views

Finding the numerical solution to a polynomial of a high degree [on hold]

I would like to numerically solve the following equation for ρ and use the obtained values of ρ to calculate the values of VR ...
0
votes
2answers
323 views

Does the equation have two roots? [on hold]

I want to solve the equation $$-x^2+\sqrt{2-x^2} \left(x^2+2 x-1\right)+2 x+5=0.$$ I tried ...
12
votes
2answers
290 views

Behavior of Reduce with variables as domain

When using Reduce, I accidentally put a set of variables as the domain. To my surprise, it not only seems that Reduce expects ...
3
votes
1answer
92 views

Roots of Whittaker W function

I am interested in finding the roots $u$ of the equation $$ W_{1,\imath b}(a)=0, $$ where $W_{\kappa,\mu}(z)$ denotes the Whittaker $W$ function, $a>0$ is a fixed parameter, $\imath=\sqrt{-1}$ and ...
6
votes
4answers
142 views

How to eliminate variables when using Solve[]

In certain problems, we need to solve systems of equations and get results in terms of just selected variables. For example, how could we solve eqn==0 below for ...
3
votes
2answers
95 views

Solve for x given an interpolation function, y

Given a list of data, lst={{x1,y2},{x2,y2},...,{xn,yn}} and the interpolation function fun, y=Interpolation[lst] which ...
0
votes
1answer
56 views

Problem using NDSolveValue

Good afternoon, fellas. Could anyone here help me solve this problem? ...
13
votes
4answers
692 views

How to make a Line[] with no end?

I'm trying to do this: In this graph, the secant points are aproximated in order to become the tangent, it seems I need some kind of function which plots a line based on two points and it's points ...
0
votes
0answers
37 views
0
votes
0answers
42 views

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), ...
7
votes
4answers
680 views

How many times do the two given curves intersect at the origin?

I'm reading/studying on my own a book about algebraic curves. I'm trying to find a way for Mathematica help me with the following (the book, ISBN: 038731802X, allows me to use any CAS / program. ...
0
votes
1answer
106 views
2
votes
1answer
102 views

Solving an integral equation numerically

my problem is: I get the result of definite integral and now I need to find the upper limit for the same integral but with opposite sign value so f2=-f1. ...
1
vote
1answer
75 views

Why can Reduce solve for Integers but not for Reals?

I'm showing as an image, since the question is generic. If we remove $m$ from the inequality we get both solutions. Why doesn't the first inequality work for both domains? Edit here is the code per ...
4
votes
1answer
145 views

Does `Reduce` give complete and necessary conditions?

I want to obtain a solution for a system of five inequalities. For instance, ...
1
vote
1answer
64 views

using FindRoot with a Module that takes a parameter

Observed an error when calling a Module from FindRoot. I created a module which first solves a differential equation and then returns the value of that differential equation when the independent ...
1
vote
2answers
77 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 ...
0
votes
0answers
27 views

How to refine the approximate solution of an implicit function? [closed]

I have an equation of the form exp(A(C-x))-1-exp(x-B(C-x)^(2/3))=0 Here A,B and C are constants, x is the unknown, I want to find, but approximate value of x is known. so, the problem is how to get ...
1
vote
1answer
74 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. ...
4
votes
1answer
152 views

What are the hidden specifications for FindRoot

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system" (or a nonlinear equation I ...
2
votes
1answer
50 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} - ...
1
vote
0answers
100 views

Using NMinimize to solve the Multi Commodity Flow problem

I have the following optimization problem and I was hoping to solve it with NMinimize. Unfortunately, I don't get the desired result. I would like to get an optimal vector for $d_{e}$. This is how ...
0
votes
1answer
57 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
votes
2answers
158 views

How can Mathematica help me to find a real radical expression for roots of this polynomial?‎

The polynomial $P(x)=x^‎‏4‏‎-‎‏4‏x^‎‏2‏‎-‎‏2‏x+‎‏1$‏‎ has ‎‏4‏‎ real roots (this can be clearly checked by plotting). But solving $P(x)=‎‏0‏‎$, using ...
1
vote
0answers
67 views

Truncated Distribution Parameter Search Produces Singular Jacobian Using FindRoot [closed]

I'm trying to find the 2 parameters of a truncated Weibull distribution using version 10 and FindRoot. I would like to truncate the distribution between t =0 and t = 3600 with the probability of ...
0
votes
0answers
41 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 $\frac{m(m-1)}{2}$ ...
1
vote
1answer
105 views
45
votes
8answers
2k views

Updating Wagon's FindAllCrossings2D[] function

Stan Wagon's Mathematica in Action (second edition; I haven't read the third edition and I'm hoping to eventually see it), demonstrates a nifty function called ...
4
votes
2answers
137 views

how to find numerical zeros of $f(z)$ in a compact complex domain

I encountered a function $f(z)$ with several zeros in a region $1<\Re(z)<2, 3<\Im(z)<4$. These zeros are visible in a three dimensional plot like ...
2
votes
2answers
80 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, ...
0
votes
1answer
32 views

Many NSolves to interpolating function

I have an expression of the form: expr = TerribleNumericalFunction[U[p]] == SimpleFunction[p] The Simple function is a ...
1
vote
1answer
60 views

Trouble using Solve and NSolve with functions involving Erf

I have the following functions: R[k_, x_, t_] := -.5*(k - x)*(1 + Erf[-(k - x)/t]) L[k_, c_, x_, t_] := .5*c*(k - x)*(1 + Erf[(k - x)/t]) I'm interested in ...
0
votes
1answer
48 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: ...
6
votes
0answers
61 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 ...