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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1answer
47 views

Presenting the solution of an equation with the form of x=

In Maple you can use {} inside the command in order to present the evaluation as x=... For instance, the command ...
3
votes
1answer
112 views

Solving an equation containing an integral in the unknowns

I have an equation of $x$ and $y$, which reads $$ -\alpha^2+\frac{2}{3} \alpha^3+y^2-\frac{2}{3}y^3+x^3f(\frac{y}{x})=0, $$ where $\alpha$ is positive parameter and $f(x)=\int (1-\tanh x) ...
2
votes
1answer
129 views

Constant Heat Flux Boundary Condition for the Differential Heat Equation

I am attempting to solve the transient heat equation for a very simple geometry and I am getting a junk solution. I have identified two distinct regions (wall and super-heated fluid layer) with their ...
3
votes
3answers
174 views

FindFit with a sophisticated function (integral)

I am trying to find a fit to the distribution function (empiricial data) in terms of a function which is itself an integral of a product of two simpler functions (two polynomials), that is the model. ...
3
votes
0answers
156 views

solve tricky nonlinear ODE on a grid

I've been working on the same question for a while now and would appreciate any advice on what I'm doing wrong or any direction on how to actually solve the problem. :) On xzczd's advice, I retried ...
3
votes
1answer
82 views

Speeding up constrained optimization problem solving

I have a problem on my homework with Lagrangian multipliers that Mathematica has now been bashing at fruitlessly for 10 minutes. I'm not sure whether I did something horribly wrong codewise, but it's ...
1
vote
1answer
61 views

Adding algebraic functions to NDSolve

I want to define an integral function which depends on a system of ODE and is also used to NDSolve the ODEs. ...
1
vote
1answer
42 views

Manipulate - strange behaviour with NSolve (I suppose)

I have written the following code for a mechanical calculation. The calculation works, but as soon as I try to use Manipulate(needed to generate a .cdf after all), ...
5
votes
4answers
236 views

Finding $y$ coordinates for $\sin(x+y)=x^2+y^2$

How can I find the $y$ coordinates of the equation $\sin(x+y)=x^2+y^2$ when $x=0.5$? I've tried NSolve[Sin[x + y] = x^2 + y^2 /. x -> 0.5, y]
0
votes
1answer
132 views

Why is my expression not a quantified system of equations? [closed]

Who can help me to understand why my code is wrong? It is giving me a message saying "is not a quantified system of equations and inequalities"?
1
vote
1answer
88 views

How to increase the precision to get the correct roots at the boundaries?

I want to solve an equation and Plot a graph of $\delta(\tau)$, where $0<\tau,\delta<1$. In principal $\delta(0)=1,\delta(1)=0$. However, when I solve the equation, the points near $\tau=1$ ...
2
votes
2answers
119 views

Solving two non-linear equations with two unknowns [duplicate]

I'm a beginner in Mathematica. I'm trying to solve : ...
3
votes
2answers
65 views

FindRoot, How to Return Null After x Number of Iterations

I am using FindRoot to find the root of a function, say f(x), and going through a loop for different values of ...
2
votes
0answers
114 views

How to solve an equation where the unknown variable is inside the integration [closed]

I have an equation: $$ \frac{1}{g}=\int_0^{\frac{1}{\delta}\sinh \frac{1}{g}} \frac{\tanh\left(0.882\, b\,\delta\sqrt{1+z^2}\right)}{\sqrt{1+z^2}}\mathrm{d}z $$ I want to obtain the relation ...
4
votes
2answers
181 views

How to solve a linear system by LinearSolve when the variables are duplicate?

Given that I have a set of equations about varible $x_0,x_1,\cdots,x_n$, which own the following style: $ \left( \begin{array}{cccccccc} \frac{1}{6} & \frac{2}{3} & \frac{1}{6} & 0 & ...
1
vote
0answers
31 views

Assign the results from a Solve to variable [closed]

I am a new user. I know, that my question was already asked billion times before, for example here, but I still cannot adopt these answers to my problem. In my problem I am solving the equation and a ...
1
vote
1answer
55 views

Newbie Issues with Solving & Plotting a System of equations

I'm having some problems with my mathematica code, I think I'm overlooking something simple. I get valid solutions for u0 thru u4, but it doesnt generate any plot at all. Also, I'd really like to plot ...
0
votes
0answers
110 views

Solving in Mathematica

I am trying to solve system of equations and inequalities in Mathematica. I am having the doubt that how much of preliminary processing should I do before solving. For example, consider a system of ...
2
votes
0answers
59 views

NIntegrate over statistical variables with parameter

Essentially, what I am trying to do is the following: Integrate a function which contains the parameter k ...
9
votes
2answers
159 views

Does LinearSolve know that I gave it a Sparse lower triangular matrix?

Let $\mathbf L$ be a nonsingular numeric (non-symbolic) large, lower triangular sparse matrix. Let $\mathbf b$ be an appropriately sized vector. I want to solve $\mathbf L\mathbf x=\mathbf b$. ...
2
votes
2answers
69 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
81 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
75 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 ...
7
votes
1answer
107 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. ...
0
votes
0answers
75 views

Solve a simple vector equation

I have a vector x = {1, 2, 3} and I want to solve for y such that 5 + x == y which ...
3
votes
2answers
114 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
59 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
59 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
81 views

Solve equation with sum in it

Have trouble to solve this equation. Anybody knows where're the problems? ...
0
votes
2answers
130 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
31 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
154 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, ...
1
vote
1answer
108 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
102 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 ...
0
votes
1answer
53 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
43 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
139 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
70 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
44 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
188 views

How to locate the position of a periodic orbit

These are the equations of the dynamical system ...
1
vote
1answer
79 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 ...
16
votes
2answers
275 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
81 views

Numerically solve recurrence equation

I have the following recurrence equation ...
0
votes
1answer
111 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
198 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
115 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
63 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
121 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
54 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 ...