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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0answers
366 views

Solve equations real and imaginary part separately

For my system of equations, the procedure described in Solving complex equations of using Reduce works no more. How can I separate the real and imaginary part of ...
2
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1answer
823 views

Error/warning when using NSolve for simple equation

I am using NSolve to solve an equation, as shown here: ...
-2
votes
1answer
188 views

Symbolic Simulations

I have 9 nonlinear equations and 10 unknowns. It is not possible to obtain a numeric solution but I do get a parametric solution. It is useful in my case because I want to observe how parameters (p1, ...
3
votes
0answers
419 views

FindRoot gives a wrong solution which obviously should not be there

I got stuck on FindRoot and I didn't see any similar problem posted, so let me explain what I am trying to do and what problem I meet here. I try to find roots of a particular function, which in the ...
2
votes
1answer
120 views

Finding the root of a nested function with small values

I have reduced an error in my program to this line of code: FindRoot[Nest[# (1 - #) k &, 1/2, 2^4] - 1/2, {k, 3.5}] It works for $2^1, 2^2, 2^3, 2^4,$ but ...
4
votes
1answer
340 views

Eliminating functions from system of PDE in Mathematica

Mathematica users, Let's see an example of three PDEs: How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
2
votes
0answers
133 views

Nest for large value of n

I am working on a problem to find the Feigenbaum constant. In this problem I have to get $f^{2^n}(1/2)$ with $f(x) = kx(1-x)$. I use Nest to get $f^{2^n}(1/2)$ but ...
2
votes
1answer
135 views

Solving a system of equations

Mathematica doesn't want to solve my exact system with 3 equations and 3 variables. ...
2
votes
0answers
146 views

Why is FindRoot initial value far from the specified one?

I am trying to numerically find the root of a function that looks a bit like: 1/x - (SchurDecomposition[A[x]][[2]])[[1]], where ...
2
votes
1answer
229 views

A basic problem with Solve

I have this equation: 4b*Cos[2t]-4a*Sin[2t]==4Cos[2t]+8Sin[2t] Which I would like to solve. Without using mathematica, you can pretty easily see that a = -2 and ...
3
votes
2answers
245 views

Mathematica does not understand (R^3)^(1/3) is the same as R [closed]

In the output from a calculation in mathematica stands a/((R^3*c)^(1/3)), with c and a ...
2
votes
0answers
280 views

Conditional statements in intial conditions?

This is potentially a daft question, but I thought I'd ask it; I have some material free to diffuse in a boundary between rn and ro; I've been able to get it working nicely for neumann type boundary ...
4
votes
1answer
464 views

How to solve this equation with integers as a solution?

I want to solve the equation $$x^y + y = y^x + x$$ with $x$, $y$ are integer numbers. I tried Solve[x^y + y == y^x + x, {x, y}, Integers] How to solve the ...
6
votes
1answer
150 views

Why is FindInstance failing when I relax a set of constraints?

I'm attempting to use FindInstance to generate coordinate sets for plausible triangles with edge length distance constraints. E.g.: ...
0
votes
0answers
218 views
0
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1answer
190 views

solution of differential equation

I have the following code that gives you a phase portrait of a 2d system and I can't understand what means the 3rd and 4th line (sol1 and sol2). ...
0
votes
1answer
93 views

Define variable relationships and dynamically update variables

I would like to define a relationship between 3 variables first and then later when I have filled two of the variables with a number, I would like to extract the value of the last value. For example: ...
0
votes
1answer
109 views

How to delete duplicate solutions of this system of equations?

I want to find vertices (has integer coordinates) of the triangle $ABC$ with the centorid is $G(1,1)$ and orthocenter is $H(3,3)$. I tried ...
5
votes
3answers
417 views

Solving a system of equations with conditions related to the number of solutions

The equation below describes a conic with oblique axis: $$9 + 22 x + 9 x^2 + 46 y + 24 x y + 16 y^2=0$$ It is a parabola, as the coefficients in $x^2$, $y^2$, $xy$ form a perfect square. To find the ...
1
vote
1answer
314 views

Solving Intervals

In a recent question I posed, it was noted that by design, Sqrt[ blah] only returns the positive branch, even though we might want to obtain all possible symbolic solutions. So, taking care to avoid ...
0
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0answers
272 views

DSolve::overdet for system of linear PDEs

I would like to resolve symbolically the following equation: ...
2
votes
2answers
320 views

How do I get the solutions of a cubic equation in trigonometric form?

I know $x^3-3 x+1=0$ has three roots that can be expressed in trigonometric form: $\{2\sin(10^\circ),\,-2\cos(20^\circ),\,2\cos(40^\circ)\}$. How can I get this result with Mathematica?
5
votes
2answers
307 views

Using RSolve correctly

I am having problems persuading Mathematica to solve even the simplest recurrence relations. As an example, how would you do the following? ...
9
votes
4answers
621 views

Finding the roots of Hypergeometric1F1[]

I am trying to find the roots, λ, for this equation: Hypergeometric1F1[1/4 (2 -  λ /β), n + 1, β] for certain ...
1
vote
2answers
2k views

Using FindRoot with an interpolating function

This question bears resemblance to a few other questions on mathematica.SE about finding points of intersection of crossing curves. I know that the guidebook of numerics has an entry about the whole ...
0
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0answers
186 views

Defining and Solving Systems of Equations Using Matrix Tables

I've defined a system of equations, but I been unable to get Mathematica to solve for the individual variables created by matrix tables. ...
3
votes
1answer
117 views

Find point at which equation stops having roots (if it exists)

I am interested in the roots of this function: f[M_, b_] := 1 - (2 M Gamma[2, 0, (1/M + b M)/Sqrt[b]])/(1/M + b M) for fixed values of b. In particular I want ...
7
votes
3answers
1k views

Finding the number of solutions to a diophantine equation

I want to count total number of the natural solutions (different from 0) of the equation $2x + 3y + z = 100$, but don't know how. How can I calculate it using Mathematica? I tried: ...
0
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0answers
186 views

Finding all roots of the system of two complex equations

I need to find all roots for the system of two complex equations. Obviously I can rewrite them as 4 real however problem remains. I have looked through routines connected with using ContourPlot ...
0
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1answer
97 views

Plotting query - same values on Y-axis / viewing data

I'm new to Mathematica, and have numerically solved two similar functions with the following code; ...
0
votes
1answer
251 views

Solving a system of equations using subscripted variables

I want to solve this equation: X(i, j) + C*Y(i, j) = Z(i, j) Where ...
9
votes
3answers
690 views

Using FindInstance to Prove No Solutions Exist

For a small amount of background, I am currently working on an undergraduate research project in Combinatorial Geometry and I'm working on a case analysis for embedding spherical simplicial ...
12
votes
2answers
1k views

How do I split up a curve into segments of equal length?

I have a curve that is defined as f[x] and what I'm attempting to do is to divide the curve into equal straight lengths for a number of segments of my choosing that I've defined as nSeg. I've created ...
4
votes
1answer
310 views

Create Euler equation

I've tried to make some research, but without any luck. How do I setup the Euler equation for this in Mathematica?: $ \text{Min} \int_0^1\left(2x^2+ \left(4t-5 e^{r \, t} \right) x \, \dot{x} + ...
4
votes
3answers
679 views

How to solve this system of equations?

I want to solve the following system of equations: $$\begin{cases} 1+\sqrt{2 x+y+1}=4 (2 x+y)^2+\sqrt{6 x+3 y},\\ (x+1) \sqrt{2 x^2-x+4}+8 x^2+4 x y=4. \end{cases}$$ I tried ...
1
vote
1answer
344 views

How to guess initial complex value for FindRoot

I have to solve a transcendental equation for a parameter, say $\beta$. Now, the $\beta$ has a range from $ik$ to $k$ where $i$ is the usual imaginary root $\sqrt{-1}$ and $k$ is a real number. ...
0
votes
1answer
154 views
1
vote
0answers
61 views

Finding Maximum Root [duplicate]

How can I find the greatest root for a polynomial if the polynomial degree is very large. One way is using NSolve. This command can find all roots in numeric. Then, ...
5
votes
1answer
142 views

Find the domain in which a sequence converges

I seem to have a lot of problems in the format of: Given the sequence $a_n=\frac{n^\alpha+1}{2n^8+5}$, for $\alpha > 0$, find the values of $\alpha$ such that the sequence converges. However, ...
8
votes
2answers
383 views

Finding all points of period n in an iterated map

I'm trying to implement an algorithm of Jenkinson and Pollicott to calculate the Hausdorff dimension of a Julia set for the map $f_c : z\mapsto z^2 + c$. It's described on page 40 of their paper, ...
1
vote
3answers
293 views
0
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2answers
221 views

Reduce on equations involving integrals

Here's part of problem from a college physics text: A time-dependent force F = (8.00 i - 4.00 t j) N (where t is in seconds) is applied to a 2.00-kg object initially at rest. (a) At what time ...
2
votes
0answers
305 views

differential equations with implicit functions

I have an ordinary differential equation that contains coefficient functions that depend implicitly on the independent variable via an algebraic equation. I am trying to go ahead and use NSolve to ...
2
votes
1answer
108 views

InterpolatingFunction with growing Domain

I want to find roots of a function that is very slow to calculate (the function itself involves a bunch of FindMaxima) so I interpolate the function in a region where I think it likely the the root ...
1
vote
1answer
175 views

Remove failed Solve[] attempts

I can't figure how to replace a failed evaluation with a null value. I am very new to Mathematica. I have an equation that are being processed using the Solve[] ...
2
votes
2answers
251 views

A While Loop with two different steps/iteration

I'd like to know if there is a possibility to solve an equation in a while loop with 2 different steps. I want the step to be small at the beginning and bigger after a certain value of sigma (sigma is ...
3
votes
2answers
240 views
2
votes
2answers
120 views

How do I generate a set of n-tuples containing integral solutions to a linear equation provided certain constraints?

Let $m,k,p$ be fixed positive integers. I want to create a table of k-tuples $(x_1,x_2,\ldots,x_k)$ comprised of solutions in positive integers to the equation below: ...
2
votes
1answer
929 views

NDSolve two PDE plus one ODE, together

I have a couple of PDE (time and space/length) that are correctly managed by NDSolve, but to which I’m adding an ODE on which the acc “accumulates”, through time, a ...
2
votes
1answer
127 views

Differentiating with respect to vectors of unspecified length

Given a function defined by f[x_,y_] := Sum[ x[[i]] (g[y[[i]]] - g[Total[y]] - Log[x[[i]]]), {i, 1, Length[x]}] I can easily calculate the derivative for a fixed ...