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

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5
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1answer
179 views

$x^6-2\varphi^5x^5+2\varphi x+\varphi^6=0$ solving in radicals

How to solve the equation $x^6-2\varphi^5x^5+2\varphi x+\varphi^6=0$ in radicals using Mathematica? where $\varphi$ is the golden ratio. Solution is Ramanujan's Class Invariant $G_{125}$, Class ...
5
votes
2answers
774 views
5
votes
1answer
285 views

A problem about Steffensen method

Two days ago,I asked a question about bisection algorithm. Thanks for Michael E2 giving me a good solution My algorithm 1, I use the bisection algorithm to generate a initial value that contain a ...
5
votes
1answer
481 views

Solving a nonlinear, second order d.e. in Mathematica

I am trying to solve the following differential equation $$ s''(x) = \frac{8}{9}s(x) -2s^2(x) + s^3(x), $$ with boundary conditions $s(-30) = 4/3 $ and $s(30)=0$, in Mathematica by using the following ...
5
votes
1answer
3k views

finding poles of a function

Is there a command to find the poles of a function $f=f(z)$? example: let $$f(z) = \frac{1}{z^2-1}$$ then we know that the poles are at $z=\pm 1$ but is there a special command in mathematica to do ...
5
votes
4answers
101 views

Using roots to get original equation

I have a list of four rules, that I would like to use to find the original polynomial that produced them. The rules are of the form ...
5
votes
2answers
1k views

Find all roots in range

Is there any way to check for all roots in a range? Jens' findAllRoots function is pretty good, but runs at approx. 10% of roots missed when I ran a quick check on ...
5
votes
1answer
167 views

NDSolve solution violates initial conditions

I have the following code: ...
5
votes
2answers
263 views

How to “ReplaceAll” using a set of conditional expressions instead of a list of rules [closed]

Suppose that I have two linear functions f[x_] := f0 + f1 x g[x_] := g0 + g1 x and a (possibly rather complicated) set of conditional expressions, obtained ...
5
votes
2answers
308 views

Computing the sign of the real part of eigenvalues in a 3D linearized system with 3 parameters

So I have this dynamical system given by: $$ \left\{\begin{aligned} x' &= a(y-\phi(x))\\ y' &= x-y+z\\ z' &= -by \end{aligned}\right. $$ where $\phi(x) = \mu x^3 - \nu x$ and $a,b,\mu,\nu$ ...
5
votes
1answer
5k 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 ...
5
votes
2answers
103 views

How to stop solving after one solution is found?

With[{P = 12}, Solve[{a^2 + b^2 == c^2, a + b + c == P, 0 < b <= a, c > 0}, {a, b, c}, Integers]] {{a -> 4, b -> 3, c -> 5}} ...
5
votes
2answers
156 views

How to find an estimated root efficiently with binary stochastic estimation of the function?

I am trying to construct certain nice geometric patterns, and one particular feature I'm trying to optimize is the balance of black and white corresponding to point being inside, or outside a ...
5
votes
1answer
153 views

Solving an identity

I am trying to solve this identity using Mathematica: $$3 \sqrt{5 \sqrt[3]{37}-16}=\sqrt[3]{a}-\sqrt[3]{b}-c $$ I know that a, ...
5
votes
1answer
81 views

Passing starting values to FindRoot when called by the Shooting Method of NDSolve

According to the documentation of the NDSolve Method -> "Shooting" option, it is possible to pass to ...
5
votes
1answer
314 views

Calculate max value

Update Using ...
5
votes
1answer
198 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, ...
5
votes
1answer
714 views

Solving recurrence relation using Mathematica defined in a piecewise way

I have a recurrence relation defined as following: RSolve[ { p[0] == p0, p[1] == λ p[0]/μ, p[i + 1] == λ p[i]/(2 μ) }, p[i], i ] Note that the relation ...
5
votes
1answer
65 views

How to solve an equation system whose equations are based on Mod[x,y]

I'm trying to find the parameters of a specific linear congruential generator (pseudo random number generator) based on a list of the first five numbers generated by it. The list is this one: ...
5
votes
1answer
387 views

Use Pattern with Vectors in Assumptions

I had a problem using Pattern with Vectors in Assumptions. Here's how I use ...
5
votes
1answer
221 views

Verify Harmonic Addition Theorem with Mathematica

I've calculated the harmonic addition theorem and would just like to check my result with Mathematica. However, ...
5
votes
2answers
609 views

Extracting Reduce results

I'm solving a Diophantine equation inside of a function using Reduce but I'm having trouble extracting the necessary parts of the answer. For example, if my input ...
5
votes
1answer
200 views

Finding and plotting roots with parameter

I have the following function: $$u(x,t)=\sum_{k=1}^\infty\frac{v_0 L}{\lambda_k c \sin\left(\lambda_k\right)}\sin\left(\frac{\lambda_kx}{L}\right)\sin\left(\frac{\lambda_kct}{L}\right)$$ and this ...
5
votes
2answers
489 views

Reducing exponential inequalities fails

I am quite stumped by this problem : Reduce[ N^(x-y) <1 && N > 0 , x, Reals] gives the expected result ...
5
votes
1answer
250 views

Incompleteness of FindInstance

I've been playing around with Resolve and FindInstance. I know that Resolve should always ...
5
votes
0answers
145 views

VERY slow to solve a nonlinear equation involving matrix eigenvalues

I am trying to solve a problem similar to the following: ...
5
votes
0answers
95 views

Find regions in which the roots of a third degree polynomial are real

I have to find the roots of a third degree polynomial in $\phi$ that depends from 3 parameters, namely $t,s,w\in \mathbb R$. In order to do that I've used the command ...
5
votes
0answers
109 views

How to find an algebraic representation

I want to find matrix representation of some algebra (Clifford algebra Cl(3,1) in this case). Here is an example, which I would like to get and then extend to higher dimensional matrices. Suppose we ...
5
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0answers
286 views

What is the algorithm behind Mathematicas Reduce in this equation?

Mathematica can use Reduce to arrive at an answer in this equation ...
5
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0answers
100 views

Using quantifiers with free indices as declarative conditions in equation solving

This is a toy example: Is there a way to rewrite Reduce[{Norm@{c[1], c[2], c[3]} == 1, 0 <= c[1] < c[2] < c[3]}, {c[1], c[2], c[3]}] ...
5
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0answers
2k views

Solve huge symbolic system of linear equations

I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
4
votes
3answers
492 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 ...
4
votes
7answers
5k views

What is the equation to plot a vertical line?

Please help. Trying to find area between three curves, e^-x, x = 2, y = 1. Can't find out how to plot x = 2. Don't want to use ...
4
votes
2answers
1k views

Can mathematica solve this equation?

I have the following Mathematica code to solve an equation coming from isoparameteric finite element for quadratic tetrahedron element. I need to get the iteroplation fast and accurate. I only find ...
4
votes
3answers
1k views

Using DSolve to solve for x[t,parameter]

I'm trying to solve an ODE with two independent variables (a cannon firing from a cliff incorporating wind resistance dependent on velocity). I've tried the following for the x-component: ...
4
votes
2answers
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?
4
votes
3answers
4k 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 ...
4
votes
3answers
553 views

Symbolic derivative of $n$-term product

I want to determine the relationship that must exist between the $x_i$ and $y_i$ such that $$ \frac{\partial}{\partial\theta} \prod_{i=1}^n \frac{f(x_i,\theta)}{f(y_i,\theta)} = 0, $$ where $$ ...
4
votes
2answers
712 views

How do I solve N simultaneous equations for N variables?

I have a function: f[x_] := x + 31 x^3 + 5 x^25 Which I want to find an expansion for: ...
4
votes
3answers
489 views

Finding parameters making real part of eigenvalues vanish

I have the following $\;3\times3$ matrix: $\left( \begin{array}{ccc} 0.04 -0.4 b & 0 & 0.04 -0.4 b \\ 0 & -0.08-1.2 b & -0.06-0.9 b \\ 1.04 -0.4 b & 2.08 -0.8 b & 0 ...
4
votes
5answers
375 views

Solve for exponents

I have this problem that I"m trying to work out: Here's my attemp: me = 0.51109991 mp = 938.2723 mpe = mp/me Solve[(2^n)*(3^mm)*(\[Pi]^p) == mpe, {n, mm, p}] ...
4
votes
5answers
352 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 ...
4
votes
1answer
2k 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 , $m_{i,j}$ ...
4
votes
4answers
4k views

Solving complex equations

I feel like I am missing a basic, but key point when using Mathematica's Solve or Reduce. ...
4
votes
2answers
931 views

How to solve for an Z-Score of a T-Distribution?

I'm looking for the Z-Score for a distribution, where the integrated area sums up to 0.90. Unfortunately I always get an error from Mathematica, ...
4
votes
5answers
590 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
4
votes
2answers
277 views

Can I solve a certain equation?

Neither Mathematica nor Wolfram|Alpha can resolve the following. How else can I reach a solution? Reduce[(1 + x)^(2/m) - (1 - x)^(2/m) == (1 - x^2)^(1/m), x]
4
votes
2answers
1k views

How to find regions that satisfy this inequality?

I am new to Mathematica and would like to find the set $$\{ (x,y) \in \mathbb{R}^2: (3x+y\exp(xy))(x-a) + (6y + x \exp(xy))(y-b) < 0 \}$$ for some constants $a$ and $b$. How can I do ...
4
votes
3answers
428 views

Solving complex equations with variable exponents

How would I go about solving $(1+i)^n = (1+\sqrt{3}i)^m$ for integer $m$ and $n$? I have tried ...
4
votes
3answers
165 views

My evaluation is taking a lot of time

I was evaluating the roots of a transcendental equation, when I noticed that Mathematica never finishes but stays in the running state. The following is the code that I was using: ...