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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2answers
73 views

how do I control the output of Reduce function?

Reduce[x*y > 50 && x*y < 100 && x < 100 && x > 1 && y > 1 && y < 50, {x, y}, Integers] what if I want ...
0
votes
1answer
58 views

Solving a polynomial where variables are constrained to take only some values

I want to find out which combinations of 1's and 0's would make this kind of equation be null: ...
0
votes
0answers
35 views

Expectation of Largest Roots of Bernoulli distributed coefficient Monomials

I am interested in determining the most probable maximum values of the real roots of polynomials of form $P(x)=\sum_{k=0}^n a_{k} x^k$ where the degree $n$ will have a defined value (say 3,4,5...) and ...
0
votes
1answer
87 views

How to solve algebra equations containing integration and parameters?

I'm trying to solve two nonlinear algebra equations for two unknown parameters, U and Tf. Since some terms in these equations contain integration, and the integration also contains U and Tf. The main ...
1
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1answer
67 views

How can I solve my system of simultaneous polynomial equations?

I want to solve the system of equations (y + 1)(a - x^p*y^q) == 0 (y + 1)x^p*y^q - c*y == 0 But I am getting the massage this system can't be solved by ...
0
votes
0answers
31 views

Why Mathematica does not Maximize when using parameter

I have recently started using Mathematica and I have got a question using it. I would appreciate if one could help me figuring out how to handle it. I have the following simple maximisation code <...
2
votes
5answers
161 views

Intersection coordinates of two spheres

I am trying to obtain a list of coordinates at which two spheres intersect. Take for example the spheres: sp1=Sphere[{0, 0, 0}, 1] and ...
6
votes
2answers
213 views

Solve a system of M equations without specifying M [on hold]

I am trying to write my game-theoretic model in Wolfram Language. There is only one remaining step and I am not sure if it is within reach of Wolfram Language (or Mathematica). I describe a simplified ...
5
votes
3answers
1k views

How can I solve the equation with integers as a solution?

I want to solve the equation $$(x-1)^2 + (y-1)^2 + (z-1)^2 = 49$$ where $x$, $y$, $z$ are integer and $x \neq 1$, $y \neq 1$, $x \neq 1$. How do I tell Mathematica to do that?
1
vote
1answer
46 views

solve equation with integer maximum [on hold]

how to solve with Mathematica a)$ \left [\kern-0.10em\left[ 5 x \right]\kern-0.15em\right] = 2x+1$ b) $ \left [\kern-0.10em\left[1/ 5 x \right]\kern-0.15em\right] > 2x+1$ EDIT = double ...
3
votes
2answers
86 views

solving PDE equation like Helmholtz equation in 2D

In my project I need to solve following equation analytically could anyone help me ? As I read the other questions, my equation seems like Helmholtz equation $$ \triangledown^2 u(x,y) - k_cu(x,...
0
votes
1answer
927 views

Solve non linear system of equations

I am trying to solve a system of two equations with two unknowns. In these equations I have, a part from constants: Unknown nr 1, $$D_{\perp}$$ Unknown nr 2, $$\omega_C$$ Known function of r: $$\mu(...
2
votes
3answers
179 views

Truncate an infinite continued fraction at order 2000

I want to solve an equation which contains an infinite continued fraction $F(n)$. Then I must (obviously) truncate this continued fraction at $n=2000$. The problem here is that Mathematica does not ...
11
votes
1answer
317 views

How to solve for the intersection points of two ellipses?

I have a parametric equation of two ellipses as follow $\begin{cases} x=a_1 \text{sin$\theta $}+b_1 \text{cos$\theta $}+c_1 \\ y=d_1 \text{sin$\theta $}+e_1 \text{cos$\theta $}+f_1 \\ \end{cases}...
0
votes
0answers
40 views

Solving linear system with non-commuting coeffcients

Is there a way to solve a linear system of equations where the coefficients do not commute? (Warning: my two-days of looking so far suggest this may be an unsolved math problem, but I figured I could ...
4
votes
2answers
245 views

Why Can't `DSolve` Find a Solution for this ODE?

I wanted to find a basis for the set of solutions of the following ODE. $$y^{''}+\frac{1}{x^2+1}y^{'}(x)+\left[-1-\frac{1}{x^2+1}\right]y(x)=0$$ But when I try to use ...
1
vote
1answer
82 views

Matrix equations solving

can you explain me the easiest way for solving this matrix equation? I have this matrix: a={{-4,1,3,0},{-2,7,1,-1},{1,-1,9,-3},{-1,0,5,-10} and the Equation is: ...
5
votes
3answers
228 views

How to get the coordinates of the intersection of two lines from a ListLinePlot?

Suppose I have two curves intersect at some point, how can I read the coordinates from the graph, not read by eye, but find it with more precision by computer. For example, here are two lists created ...
3
votes
1answer
70 views

Generating plane equation from LinearSolve

I will ask a simple question and might have an issue on the site that explains better about it, but not found. I am formulating a code that defines me an equation that I can generate a plot. ...
1
vote
1answer
71 views

getting a following error,large data points,desired output-best fit to expt. data sets

I am trying to carry out list operation but running into a following error I have large data sets(more than 0.2 million data points) and desired output will be a best fit (numerical data points ) to ...
1
vote
1answer
41 views

Splitting Logical Expression in list of expressions

I have long results of a Reduce statement in the form of {(expr1) || (expr2) || (expr3) || ...} I am looking for a way to split ...
0
votes
1answer
83 views

Solving a System of Simultaneous Equations [duplicate]

I have the command: Solve[{Cos[η] == Sqrt[3/6], Sin[α] Cos[η] == Sqrt [1/6], Sin[α] Sin[η] == Sqrt [2/6]}, {η, α}] I get the output ...
1
vote
0answers
51 views

NSolve and FindRoot failing to evaluate

So I am integrating a Piecewise function and then using NSolve to find out where the limits of integration lie to satisfy an ...
2
votes
1answer
66 views

Finding input of the function $f(a,b,c) = (d,e)$ such that $|d-e|$ = constant for $d\in[d_0,d_1]$

The actual question contains a few more parameters than mentioned in the title, but the idea will remain very similar. Lets begin abstractly; I have a certain function $f(a,b,c) = (d,e,g,h)$. I am ...
0
votes
1answer
53 views

Find the minimum of several functions

I have 6 functions of four variables $ f_i: \mathbb{R}^4 \rightarrow \mathbb{R},\, i \in 1..6$ For each function $f_j$ I want to find the subset of $ \mathbb{R}^4 $, called $S_j$, for which it is ...
26
votes
5answers
28k 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
votes
0answers
62 views

solving a set of 10 non-linear system of equations

I have a system of equations and I want to solve it to get a1, a2, b1, ...
0
votes
0answers
31 views

Making function that returns output of FindRoot [duplicate]

I'm trying to make a function that returns the solution to an equation which involves three variables, where the input variables for the function are the other two variables. So far, it runs, but ...
2
votes
2answers
255 views

Incorrect numerical derivative of function that uses FindRoot

I am trying to plot the derivative of function g[x] below where g[x] is defined as the root of another equation. However, I am ...
1
vote
2answers
154 views

After NumberForm I cannot apply a Sine function. Why?

After NumberForm I cannot apply a Sine function. Why? This works: sol1 = x /. Solve[x^2 - 3 == 0, x] Sin[sol1] Output = $\{-Sin[\sqrt{3}],Sin[\sqrt{3}]\}$ Also ...
0
votes
1answer
76 views

Module output rules like Solve FindRoot etc built-in functions

How do I print rules {x -> values} as an output from my module? I'd like it formatted just like those from the built-in functions, so that users can use Out[ ] or % to directly apply the rules. ...
3
votes
1answer
231 views

How to change parameters to equations of physical properties they belong to in an equation?

First off, I want to apologize for my poor English as I am not a native speaker. In my physics research, I had to solve a system of equations, from which I would get a solution for the speed of an ...
0
votes
0answers
89 views

Help numerically solve this non-linear PDE with singularity

I have trouble finding a numerical solution to the partial differential equation below. It seems to be a singularity in the solution somewhere, so I searched online and found that it is suggested to ...
3
votes
2answers
69 views

Using Solve[ ] inside a Module

I want to use Solve[] inside a Module. If I make the variables solved for local to the module, they are treated differently than ...
0
votes
1answer
154 views

Given $y$, find the $x$ value of a point on a Bezier curve

I have linear equation of Bezier curve with one control point: f[x_] := (1 – t)^2 x0 + 2 (1 – t) t x1 + t^2 x2; f[y_] := (1 – t)^2 y0 + 2 (1 – t) t y1 + t^2 y2; ...
0
votes
2answers
36 views

Solve inside of InputField is not dynamic

On the 7th line, I have an InputField that I want to dynamically change as I change the input. It solves an equation that is later used to determine the change in y intercept in the graph. However, ...
1
vote
1answer
49 views

Using solution of an equation [duplicate]

I want to solve something like f(x)=0 and then have the real solution be set as the value of another variable. I can't figure out how to do it. I tried something like this as an example, but it didn't ...
5
votes
1answer
263 views

Finding an analytic solution of a cubic equation

I have been trying to solve a cubic equation $$y=zy^3 + z$$ in $y$ – that is, my desired result is a function $y(z)$ satisfying the equation. Now, there are three solutions of this equation and ...
3
votes
2answers
173 views

Randomly generate points on a van der Waals surface

I'm looking to randomly place an atom $\mathbf{A}$ onto a van der Waals surface formed by atoms $\mathbf{B}$, such that the distance between the randomly-generated atom $\mathbf{A}$ and the nearest ...
0
votes
0answers
3 views

Is this equation true? [migrated]

As the question states, does this equation hold true? $\sum_{j=0}^n \sum_{E \in {n \choose j}} (-1)^{|E|}(n-|E|)! = \sum_{j=0}^n(-1)^j(n-j)!{n \choose j} $ From what I understand, this holds true at ...
1
vote
0answers
97 views

how to solve a high-dimension system faster, please

I want to solve a high-dimension system as below. If the size is 50, there are 50^2 equations and find the root cost about 6s in my PC. If the size is 100, about 100s. But if size is 500, the time is ...
9
votes
3answers
2k views

NDSolve with vectors

I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
0
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0answers
34 views

NSolve on a function with NIntegrate

I have a function defined with an NIntegrate. The function is of x,y,z, integrated across t: ...
0
votes
1answer
43 views

Solving a system of integral equations

Is it possible to solve a system of integral equations in Mathematica? More specifically, I would like to obtain numerical solutions for $\mu$ and $\sigma$ from the following system: ...
4
votes
2answers
143 views

Solution of a System of Equations Using `Solve`

Part 1 I am trying to solve a simple system of equations as follows Solve[{A x^B == f, A y^B == g}, {A, B}] But I just get the error Solve::nsmet: This ...
0
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0answers
32 views
0
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1answer
62 views
0
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2answers
45 views

Find a solution to a set of equations, within a specified range

Given the following list myList = {a + 2 g, -2 c d - 3 b f + 2 a g, d^2 f - c d g, -2 c^2 - a f, c d f - c^2 g} of five expressions in the variables ...
6
votes
3answers
207 views

Approximate analytic solution to a polynomial equation

The analytic solution of the equation $$ 1-\frac{2M}{r}+\frac{Q^2}{r^2}-\frac{\Lambda}{3}r^2 = 0 $$ obtained by using the code ...