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

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2
votes
2answers
80 views

Solving a system of vector equations

I had a problem where I had to solve a series of equations where some of the variables can take multiple value such as shown below ...
1
vote
1answer
90 views

Find Values of a and b for a Limit

I am having trouble finding the values of a and b for which $\lim \limits_{x \to 0}$ $(\frac{\sin (ax) + bx)} {(x^3)}) = -32/3 $. In Mathematica I have entered: ...
1
vote
2answers
98 views

Evaluation to true using DSolve - syntax errors?

Probably a stupid question, apologies, but I am getting an annoying error when I try to evaluate the following simple PDE $\frac{\partial C}{\partial t} = d \frac{\partial^2C}{\partial x^2}$ between $...
8
votes
2answers
131 views

Numerical solve question

Why does this work? Solve[5 Tan[t] + 9 == 0 && 0 <= t < 2 Pi , t] {{t -> π - ArcTan[9/5]}, {t -> 2 π - ArcTan[9/5]}} But this doesn't. <...
3
votes
2answers
180 views

How do I solve for a variable inside a sum but independent of the summation index?

How would I go about solving the following for c? Solve[0 == Sum[(t[i]*m[i] - c*t[i]^2)/s[i]^2, {i, 1, n}], c, Reals] I get ...
0
votes
1answer
76 views

Reducing solutions of Sin[2t] Sin[t] == Cos[t] to a simpler form [closed]

I evaluated Solve[Sin[2 t] Sin[t] == Cos[t] && 0 <= t < 2 Pi, t] And got these results. ...
3
votes
0answers
85 views

Extending Bresenham's algorithm for subpixel rendering

Original Bresenham's line drawing algorithm it limited to drawing lines between two integer pixel positions and does not allow subpixel rendering. However with my reformulation of this algorithm as a ...
0
votes
1answer
98 views

Solve equation with sum in it

Have trouble to solve this equation. Anybody knows where're the problems? ...
0
votes
2answers
172 views

Bifurcation diagram for 1D ising model

I'm new in Mathematica, I want to plot a bifurcation diagram for a complicated Ising system with dynamics that I'm working on, but to get familiar with how to perform it on Mathematica I wish to start ...
0
votes
1answer
32 views

$Failed when naming the variable x [closed]

Total beginner here, the problem goes away when renaming x into other letters. Below is the code ...
7
votes
2answers
160 views

Unexpected warning from DSolve

I'm trying to solve this differential equation with respect to $x$ $$ \frac{d^2y}{dx^2}-\bigg(\frac{dy}{dx}\bigg)^2-\frac{1}{x}\frac{dy}{dx}=\frac{1}{x^2} $$ With boundary condition $y(1)=2, y'(1)=-...
1
vote
1answer
279 views

How to solve trigonometric equations

I have the following problem: I need to solve the equation: $$\frac{\cos\left(x\right)}{x^6} - \frac{6 \sin\left(x\right)}{x^7}==0$$ and I don't really remember how to do it symbolically. Some help ...
1
vote
0answers
133 views

Solving a functional equation

Suppose I have two functions f[x,y,z] and g[x,y,z], both analytically defined. I want to solve for a function ...
1
vote
2answers
88 views

Stuck in solving two variables from two expressions

After doing experiment with Michelson interferometer I need to calculate two coefficients: k and n. This involves solving two equations for k and n: $$\frac{(8 \pi d)}{\lambda }{kn}=\frac{\text{$\...
0
votes
1answer
60 views

Help me solve this equation; I believe this is a transcendental equation [duplicate]

please can someone help me solve (x*L)+B*tan(x*L)=0, solve for x when B=10;L=0.1. The equation looks innocent but I need to find 1st 5 roots of equ.
0
votes
0answers
83 views

Solve Always with Assumptions

How can I use the Solve Always function imposing some assumption on the parameter space of the symbolic variables? Thanks!
1
vote
2answers
168 views

Code for Newton's Method [closed]

I'm trying to write a program for finding the root of f(x)=e^x+sin(x)-4 by Newton's Method but I'm instructed to not use the built in function and write the code from scratch. I'm pretty new to this ...
0
votes
1answer
74 views

System cannot be solved with methods available

I'm trying to solve the following equation, but the command Solve hasn't been successful so far. Any ideas? ...
2
votes
0answers
48 views

speeding up Solve(ing) the Diophantine equation

Trying to solve the Diophantine equation (or variation?) using Solve in order to generate some chemical formulas. I need to generate all possible solutions. The ...
7
votes
2answers
234 views

How to locate the position of a periodic orbit

These are the equations of the dynamical system ...
1
vote
1answer
94 views

Fixed points of x sin 1/x

What is the best way to find all the fixed points of f(x)=x sin 1/x? I know it has infinitely many fixed points, so there would in theory be infinitely many outputs. What can Mathematica do about this?...
0
votes
1answer
101 views

How to solve this example `x^2=2^x`? [closed]

How to solve this? I don't know, and ask you )) $$ x^2=2^x; $$
16
votes
2answers
300 views

How to implement Bresenham’s algorithm as a system of equations?

Bresenham's line drawing algorithm is usually implemented via loops. But in Mathematica we can take advantage of its ability to solve Diophantine equations. From educational viewpoint it is quite ...
3
votes
1answer
112 views

Numerically solve recurrence equation

I have the following recurrence equation ...
0
votes
1answer
213 views

NSolve not working [closed]

I'm sorry if this is a dumb question, but for some reason NSolve isn't working for me. Here's what I'm trying to do. ...
1
vote
3answers
210 views

Solve didn't give the right solution

I've got a pretty simple equation set here but I cannot seem to solve it correctly. ...
0
votes
1answer
121 views

Solving a system of non-linear equations with symbolic parameters

I'm in the middle of preparing my master thesis, where I need to find a closed form or a numerical solution for the system below. Solve[] and ...
1
vote
0answers
66 views

“Reduce” works fine for a non-linear system with 9 equations, but cannot solve it if 10 equations. Any ways to improve the code?

I am trying to solve a class of problems, which are basically about a solution to a system of non-linear equations subject to the constraint that some subset of solutions must be non-decreasing. I ...
1
vote
2answers
131 views

How can I illustrate the solution space of these equations in 3D?

I would like to plot the solution space $\{\theta,\varphi,\Omega\}$ of this vector equation, $$\begin{pmatrix} \sin (\theta ) \sin (\varphi ) \sin (2 \pi \Omega )-\sin (2 \theta ) \cos (\varphi ) \...
0
votes
1answer
73 views

Solve 4 equations using Solve [closed]

I'm trying to solve $4$ systems of equations with $4$ unknowns. There are some trig involved and I keep getting error "Solve::ifun: inverse functions are being used by Solve." Please help me to ...
4
votes
1answer
104 views

Inverse of parametrized ellipse area

If you parametrize an ellipse (with the center, not a focus, at the origin) as: {a Cos[t], b Sin[t]} the area traced out from the focus (not origin) for a given $...
2
votes
2answers
73 views

How to use the variables from Table in calculation

New to the site and Mathematica. I'm trying to use the finite element method to get a temperature profile. So if $q_0=f(T_0,T_1)$, $q_n=f(T_{n-1},T_n)$ and we also know that $T_1-T_0=T_2-T_1=T_3-T_2=\...
1
vote
1answer
90 views

How to solve nonlinear equations involving integrals

Sorry, if this is a duplicate, I was not able to find a corresponding answer. The only question related to mine, as far as I can see it, is this one: How to solve algebra equations containing ...
2
votes
2answers
118 views

Solving coupled ODEs with NDSolve to fit experimental data

I need to fit a multi-exponential data (Intensity x Time) using a model consisting of three differential equations. I want to find the parameters that gives the best fit to the experimental data. ...
3
votes
3answers
200 views

Not getting expected result from numerical evaluation of solution given by Solve

Let $m$ be a large integer and $z\in (0,1)$. I want to find $0 < k < m$ such that $\frac{\sqrt{5-\frac{4k}{m}}-1}{2} + \frac{m-\frac{k}{2}\sqrt{5-\frac{4k}{m}}}{m^2\sqrt{5-\frac{4k}{m}}}$ is ...
3
votes
3answers
265 views

How would I write iterative code to try multiple coefficients for an equation?

So, I'm trying to solve a class of equations, and get all the solutions in a list. The general form looks like this: c == a*Sqrt[1-n] PlusMinus[b * Sqrt[n]] ...
22
votes
1answer
352 views

Fast calculation of discrete logarithms

Does Mathematica have any built-in fast algorithms for calculating discrete logarithms over $(\mathbb{Z}_p)^\times$ (the group of integers modulo $p$)? Essentially, for a fixed large prime ...
1
vote
1answer
77 views

Find where a function does not depend on one of its argument

Say I have a function $f(x,y)$ with $x$ and $y$ in some domains. How do I find the subdomain in $y$ for which $f$ does not depend on $x$. My special case one could consider as an example: I have ...
0
votes
1answer
115 views

Problem in solving a simple Laplace equation

I am trying to solve the following Laplace PDE in MMA: $$\frac{\partial^2 T}{\partial x^2}+\frac{\partial^2 T}{\partial z^2}=0$$ subject to the boundary conditions: $$\frac{\partial T}{\partial z}|_{...
1
vote
1answer
368 views

How can I use Mathematica to solve a Stefan Problem using an explicit scheme?

I would like to plot the temperature distribution for a particular case. the problem is stated in the paper, behind a paywall here, summarized as Consider a one-dimensional container of length l, ...
0
votes
1answer
33 views

Solving and replacing solution for solving again

Given some equation to solve S1=Solve[f[x,z]==g[x,z],x]//Simplify which produces something like x->xsol[z] I write ...
1
vote
1answer
143 views

Finding equilibria to a system of 3 ODEs with 11 unknown parameters. Looking for the intersection of 3 surfaces

I have the following system of 3 ODEs of 3 variables $(\ell,M,h)$ and 11 parameters $(\sigma_{\ell},\mu_{\ell},d_{\ell},\sigma_M,\alpha_1,\beta,\alpha_2,\nu_M,\sigma_h,\nu_h,d_h)$: $\frac{d\ell}{...
1
vote
4answers
121 views

Build a truncated tower with numbers from 1 to 9 without repeating

consider the image subject to the following conditions appearing in my code, I find not the appropriate numbers ...
4
votes
2answers
140 views

Different results from Solve depending upon the solution variables listed

Here is a very simple set of equations to solve: ...
2
votes
0answers
76 views

Solve vs. LinearSolve - ill solutions using both methods [closed]

I'm wishing you a nice day. My question is related to this question previously asked by me, answered by PlatoManiac. Although I found a bug in his post I decided to leave his answer accepted and ask ...
0
votes
3answers
68 views

Problem with Solve for simple equation

I have a simple question, but just can't figure it out. I have the following model equation to get a peak. I want to get the the two t-values on the left and right side of the peak, where the model ...
2
votes
1answer
96 views

Plot the result of Solve for multivalued solution

I would like to plot the (most likely) multi-valued solution to an equation, as I vary one of the parameters. Here's my approach: ...
13
votes
1answer
794 views

Nonlinear FEM Solver for Navier-Stokes equations in 2D

it's me again. I'm trying to obtain a numerical solution to Navier-Stokes equations in 2D in a non-rectangular region. So far, this guide was very helpful, but he is using finite differences, which is ...
0
votes
0answers
26 views

Is it possible to assign the result of Solve command to the variables? [duplicate]

I am having a hard time with a huge script. I use Solve function to solve my algebraic equation with parameters of the 4 th order. The result is really messy. Is ...
1
vote
1answer
210 views

Differential equation solution

DSolve[y''[x] + (a - (b*x^2 - c)*x^2)*y[x] == 0, y[x], x] I couldn't solve this equation, please help