Questions tagged [equation-solving]

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

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2
votes
1answer
845 views

How to solve simultaneous equations faster with Compile?

I have large 6x6 matrix Uwhich is a multiplication of 15 rotational matrix. All of the elements are Sin\[theta] and ...
2
votes
3answers
424 views

equation solving problems

I have some equation: $$ veq=-2-lr-l^2r+2(r+ir^3\omega) v' + (-2+r)r^2v'^2 + (-2+r) r^2 v''==0 $$ or in Mathematica form: ...
6
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2answers
578 views

Reduce and Solve unable to solve equation

I have the following equation. Why aren't Solve and Reduce able to find the solution? ...
3
votes
2answers
795 views

Is there a way to solve the Apollonius Circle problem in Mathematica?

Assuming x, a, and b are complex numbers, is there a way to reduce the equation Abs[x - a] == k Abs[x - b] to something like ...
5
votes
2answers
3k views

Solving a trig equation

I am trying to find an explicit solution to a trigonometric equation. It is running for a long time and I didn't get any result, but Maple solves it quickly. Why ? ...
4
votes
1answer
1k views

Solving Simultaneous Equations

I am trying to solve two equations that take the form: $W_0 \sqrt{1+\left(\dfrac{z}{\lambda\,\pi\, W_{0}^2}\right)}=W_1\;\,\quad \ldots(1)$ $W_0\sqrt{1+\left( \dfrac{z+0.1}{\lambda\, \pi\, W_{...
2
votes
1answer
448 views

How to solve a symbolic equation with symbols in powers

I am trying to solve $\dfrac{\rho\ ((1-b)\ \lambda _f\ \lambda _s\ P _A)^{\rho }}{b-1}+\dfrac{\rho \left(\dfrac{b\ \text{ps}\ x}{1-\text{ps}}\right)^{\rho }}{b}=0$ in terms of $b$, I ...
6
votes
1answer
1k views

Reduce an equation by putting a new variable

I have the following equation given: $$ (26-x)\cdot\sqrt{5x-1} -(13x+14)\cdot\sqrt{5-2x} + 12\sqrt{(5x-1)\cdot(5-2x) }= 18x+32. $$ In order to solve it, I want to substitute $t = \sqrt{5x - 1}-\sqrt{...
15
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1answer
1k views

Why does repeating an equation help in FindRoot?

I'm trying to understand this behavior of FindRoot. Consider a sample function (the one I'm actually interested in is far more complicated, but has similar issues) ...
0
votes
1answer
552 views

(N)Solve does not solve equation

I am trying to calculate where a beam hits a mirror. The mirror is described by this curve (two facing spherical mirrors): ...
5
votes
2answers
295 views

Solve for $a$ as a function of $\beta$?

I am trying to solve this equation: $$\beta^{-a} \Gamma(a) \sin(a \pi) + e^\beta \beta^{2 a - 1} \Gamma(1 - a) \sin(a \pi) = 0$$ I tried the following: ...
0
votes
1answer
490 views

Iterative way to find roots of confluent hypergeometric function [duplicate]

I am trying to find roots of confluent hypergeometric function and I wonder if I can choose the initial guess by the choice of $\beta$. ...
16
votes
5answers
2k 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 ...
2
votes
1answer
1k views

Using previous two solutions as a start point in FindRoot

I need to solve a sequence of equations and I want the starting point of each new FindRoot to be the solution of the earlier FindRoot, increased or decreased by a a bit in the following way: Some ...
9
votes
3answers
3k 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: ...
33
votes
2answers
16k views

Marking points of intersection between two curves

I'm trying to illustrate the solutions numerically and graphically for an equation such as Tan[x] == x. I think I did everything ok except I wanted to mark each ...
3
votes
1answer
1k views

wrong use of _?NumberQ?

I am having trouble with a numerical exercise. Here's a simplified version of my problem. I define two functions to find the solution to two constrained maximization problems: ...
6
votes
3answers
534 views

Why don't I get numeric values from this Solve?

Solve[ a^2 + b^2 == c^2 && a < 100 && b < 100 && c < 100, {a, b, c}, Integers] gives me this result ...
2
votes
1answer
2k views

FindRoot inside Table

(MWE at the end of the post) I need to solve a non-linear equation $f(y;x_1,x_2,..,x_5)$ in one variable $y$ and then compute 4 new output expressions, for over 60 different initial parameter inputs ...
8
votes
3answers
3k 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?
2
votes
1answer
1k views

FindRoot Infinite expression 1/0 encountered error

I have 1 equation in 1 variable, which when I use Plot, looks like this: ...
4
votes
1answer
1k views

Selecting polynomial roots and plotting against parameters

An implicit function $f(x,k)=0$ is quadratic in $x$ and contains one parameter $k$ which I must vary. Using Solve, I get two real solutions for each specific $k$: $...
21
votes
2answers
7k views

FindRoot Domain restriction

I am solving a system of four non-linear equations in four variables using FindRoot. I have some sense of the relationship between the variables so I don't want Mathematica to do its computations in ...
3
votes
2answers
1k views

Numerically Solving two dependent Transcendental Equations

I need to solve a system similar to the following (Except it is quite large. Solving this ought to do the job): $$ \tan[2f(t)] = 1+ t^2\ $$ and $ f(t) $ is $ k $, such that$$ \tan[2kt]-(1+k^2) = 0\ ...
8
votes
3answers
2k views

How to find the maximum value of an integer that satisfies some inequality

Consider the following Mathematica expression: Reduce[2^j/(j + 1) <= 10, j, Integers] which outputs: ...
4
votes
1answer
480 views

pH calculations, speeding up code involving Solve

I'm trying to calculate pH values of solutions containing water and acetic acid. The relevant equations have been defined and I now want to find a solution using Mathematica. For a specific acid ...
2
votes
1answer
4k views

Solving a system of equations in two variables

I have a system of two equations in two variables $x$ and $y$. $$\begin{align} F_1(a,b,c,d,e)x+F_2(a,b,c,d,e)y+F_3(a,b,c,d,e)&=0\\ G_1(a,b,c,d,e)x+G_2(a,b,c,d,e)y+G_3(a,b,c,d,e)&=0 \end{...
4
votes
3answers
576 views

How to obtain a fixed number of solutions to $x+y=1$?

How to obtain a fixed number of solutions to $x+y=1$? For example, I want 4 solutions: $(1,0),(2,-1),(3,-2),(-2,3)$ I want to do this also on bigger equations such as $x+y+...=1$ and then I want to ...
7
votes
1answer
2k views

Efficient implementation of cubic equation of state

...In this case the Peng Robinson Equation of State. Equations of state are empirical equations with parameters derived from experimental data. They are used to predict pure component and mixture ...
5
votes
1answer
13k views

Can Mathematica help to rearrange an equation?

I have an equation which I want to rearrange so one variable is on the left side by itself. Normally, I would do this with basic algebra and identities. However, is it possible to use Mathematica to ...
15
votes
1answer
519 views

Strange behaviour of Reduce for Mod[x,1]

For every integer $x$ the equation Mod[x, 1] == 0 holds. While Simplify[Mod[x, 1] == 0, Element[x,Integers]] gives ...
11
votes
2answers
2k views

Trying to fit an unknown extreme distribution

First up, I'm quite new to Mathematica so any hints on better code would be greatly appreciated. I have some histogram frequency data from an unknown distribution that I'm trying to fit. Here's the ...
5
votes
1answer
4k views

Solve system of equations related to perspective projection

I'm trying to solve system of equations. I have 4 points before perspective projection and after and I whant to obtain matrix of perspective projection $m_{i,j}$ ($x,y,u,v$ are known , $m_{i,j}$ ...
2
votes
1answer
7k views

solve non-linear system of equations

I have a system of equations and I want to solve it to get x, y $$\begin{cases} u= C_{1}+(x-C_{1})(1+k_{1}((x-C_{1})(x-C_{1})+(y-C_{2})(y-C_{2}))) \\ \\ v= C_{2}+(y-C_{2})(1+k_{2}((x-C_{1})(x-C_{1})+(...
3
votes
2answers
191 views

Why didn't Reduce give me the right result?

My code: Clear[r1, r2]; par[r1_, r2_] := r1 r2 / (r1 + r2); Reduce[{5 par[r2, 32000]/(r1 + par[r2, 32000]) == 1.8 && par[r1, r2] == 5000}, {r1, r2}] ...
1
vote
1answer
3k views

Solve matrix equation A*X=X*B using LeastSquares

I want to solve matrix equation A*X=X*B using LeastSquares method, but it is suited for equation like A*X=B. All matrices are 3x3 ...
1
vote
2answers
4k views

Find the dimensions of a cylindrical can that will minimize the cost of the material

A cylindrical can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can. This is a standard calculus problem. The volume of the ...
9
votes
4answers
1k 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 ...
6
votes
1answer
2k views

How Can I use Solve/Reduce Output

Suppose I want x and y to be rationals Solve[ x^2 + y^2 == 1, {x, y}, Rationals] I am ...
21
votes
2answers
3k views

How do I split up a curve into chords 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 ...
6
votes
2answers
526 views

How to work out the parameter in a definite integration which has an exact value while the integration doesn't have an analytical solution?

Here is the equation I'm trying to solve: NIntegrate[1/(E^(1/(λ T)) - 1), {λ, 200, 220}] == 1000 T is the parameter I'm ...
5
votes
1answer
287 views

Incompleteness of FindInstance

I've been playing around with Resolve and FindInstance. I know that Resolve should always ...
6
votes
1answer
521 views

Buggy Reduce/Resolve function?

It seems to me that this is a clear-cut case of Mathematica actually producing the wrong answer (with no warnings). I'm trying to express the fact that for any integer, there exists a factorization ...
4
votes
2answers
5k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
11
votes
3answers
2k 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 2-...
3
votes
2answers
5k views

How to plot an inequality?

I need some help in plotting the following inequality using Mathematica: $$\frac{1+(x/100+0.1)\times y/100}{1.15+1.15\times(x/100)\times(y/100)}\geq 1$$ assuming $x,y\in \mathbb{Q}$, the set of ...
17
votes
2answers
2k views

Getting an InterpolatingFunction from a ContourPlot

I have a function, say minimizeme[Ω_][β_][ϵ_] = ϵ^2 Ω - Log[2 (Cosh[2 β] + Cosh[2 β ϵ])]/(2 β); I want to find its critical points in $\epsilon$ for a given ...
11
votes
3answers
355 views

Problems Computing (in a reasonable amount of time) Solutions to a System of Inequalities

For my Cryptography research I am interested in finding solutions to the following inequalities in terms of $r$ and $s$, where $p$ is some fixed constant. $$\begin{align} 2^{p - s + 4} + 2^{p - r} + ...
1
vote
2answers
701 views

solving for one solution to a system of polynomials

I'm trying to solve a system of equations: ...
7
votes
3answers
4k views

Why won't Mathematica Solve a set of two equations for one variable?

For example, if I try to Solve this set of equations Solve[y == 3 x + 5 && y == -x + 7, {x, y}] Mathematica gives the right values for ...