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

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1
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1answer
106 views
45
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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
82 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
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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
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1answer
50 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
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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 ...
1
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0answers
72 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? ...
18
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5answers
14k views

Assign the results from a Solve to variable(s)

I understand Mathematica can't assign the results of a Solve to the unknowns because there may be more than 1 solution. How can I assign the 4 values of following result to variables?
0
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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
votes
2answers
79 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 ...
19
votes
4answers
807 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? ...
3
votes
2answers
298 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
73 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
1
vote
1answer
326 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 ...
2
votes
3answers
115 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 ...
2
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1answer
72 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 ...
0
votes
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
votes
1answer
50 views

Question about a catalytic equality?

I have a question on math.SE that explains how I came up with these equations. ...
1
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2answers
182 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
votes
1answer
41 views
4
votes
5answers
226 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 ...
3
votes
2answers
176 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( ...
0
votes
1answer
50 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} - ...
0
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0answers
60 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
1answer
82 views

Tree-like nesting of function

Is there an elegant way to nest a function in a similar fashion to tree graphs; i.e., create and follow branches until some criterion is met (until we reach a leaf)? An example: We want to ...
0
votes
1answer
47 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 ...
0
votes
0answers
43 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
92 views

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

I am having difficulties getting this code to work. Code: ...
3
votes
1answer
142 views

Root finding: zeroes of Mathieu function

I am finding the roots of the Mathieu sine function, and find Mathematica and Maple do not agree on the solutions. For example, consider the solutions of ...
0
votes
0answers
51 views

Computing the coefficients for Gaussian integral

I wrote a small script to find the Gaussian integral points and weights: ...
0
votes
0answers
55 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
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1answer
61 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 ...
0
votes
0answers
20 views

Solving (one variable) Linear Equation by Dividing Slope by Constants Accumulation? [migrated]

I've been Google searching for this, and apparently my Googlefu is not strong today, or I'm doing something wrong. I have been told that it is possible to solve a one variable linear equation by first ...
1
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1answer
74 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
81 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
votes
1answer
100 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 ...
1
vote
2answers
142 views

Problems finding intersection points between line and generic function

I'm trying to find Intersection points between a line, which is given by 2 points, and a generic function (I want it to be able to handle polynomial functions, circles/ovals, lines and all ...
2
votes
1answer
74 views

Equation involving hypergeometric functions

I want to solve this equation but nor NSolve nor Solve are able to do this. ...
0
votes
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
votes
1answer
56 views

Elements inside arrays seem to be strings rather than signed numbers

When I have code like b = Array[Subscript[be, #] &, {3, 1}] b = b /. {Subscript[be, k_] :> Subscript[-be, k] /; k > 1} I am noticing that Mathematica ...
0
votes
0answers
36 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 ...
1
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0answers
43 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
votes
1answer
52 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
votes
1answer
65 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
31 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 ...
0
votes
1answer
87 views

In which condition releated to thee coefficients some equation has a solution

Please excuse me if the question seems to commonplace. Can Mathematica give a response to this question: In which condition related to the coefficients $c>0, \, n\geq 2, 0<p<1,\, a>c$ ...