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

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2
votes
0answers
167 views

Using WhenEvent for derivative of discontinuous function

I have a discontinuous function ($u(t)$, a square wave) and I would like WhenEvent to trigger when the signal goes high/low, i.e. when the value of $u(t)$ changes. ...
1
vote
0answers
68 views

Is it possible for Mathematica to give the step by step process of Reduce command? [duplicate]

Input: Reduce[3 x^2 - 2 a x + a^2 - 1 >= 0 && x > a, x] // TraditionalForm Output: ...
1
vote
2answers
363 views

Finding shortest non-zero vector $x$ satisfying $Ax=0 \pmod q$

Let $n$, $m$, and $q$ be positive integers (with $m > n$), and $A$ be a matrix over $\mathbb{Z}_q^{n \times m}$. Using Mathematica, I want to find the shortest non-zero vectors $x \in ...
0
votes
1answer
123 views

How to simulate a multivariate recursive system from a list

New to mathematica, trying to use Eric Swanson's Pertubation AIM program to solve DSGE models. His code produces a solution as a list or a table. My question is how do I use this list to simulate the ...
1
vote
1answer
132 views

Simple rule appears not to work

I have the following simple code ...
0
votes
1answer
295 views

Solve equation containing conditions (If expressions)

I want to solve the underneath equation. If I try Solve[AAA,dc], then I get no solution. Can anybody explain this? ...
9
votes
1answer
239 views

$1 - \sqrt{5}$ $\in$ $\mathbf{R}$?

Why is there a difference in the output of the following codes? First: ...
1
vote
1answer
135 views

Problem about Solve

See this example : ...
3
votes
1answer
1k views

Finding intersection of two graphs

Here is a toy problem: I have a (directional) line that starts from {2,0} and goes through {1.8, 0.01}. Also I have a ...
0
votes
0answers
52 views

Degeneracy problem at the start of a series expansion

I am facing the following problem : I have an equation which could write $$ F(x_1(Y))-F(x_2(Y)) = 0 $$ $x_1$ and $x_2$ are the largest and smallest roots of a cubic equation; their definition ...
11
votes
4answers
519 views

How can I find all values of $m$ such that my cubic equation has three different positive solutions?

I want to find all the values of $m$ such that the equation $$-m^3 + 2 m^2 x + (-2 m - 1) x^2 + m + x^3=0$$ has three different positive solutions. I tried ...
3
votes
3answers
205 views

Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
1
vote
1answer
176 views

FindRoot equation-variable mismatch

I cannot figure out why FindRoot doesn't work and returns this error: The number of equations does not match the number of variables in ... My problem: drawing ...
3
votes
1answer
460 views

How do I solve $1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x))= 0$?

Consider the equation $$ 1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x)) = 0 $$ where $A,B \in \mathbb{R}$ are constants. What is the analytic solution?
1
vote
1answer
143 views

Changing ParametricNDSolveValue options for only part of the run

Here is an example of the system that I am running, ...
0
votes
2answers
155 views

Unexpected complex roots from solving a cubic

I am new to Mathematica and there is a behavior that I don't understand. When I insert the code: Solve[-(x - 2)^3 + 10 x - 10 == 0, x] I obtain: ...
0
votes
0answers
97 views

Optimization for complex inequalities

I want to check when the expression $$ \sqrt{\sqrt{\lambda^{2}\left(2E+\lambda^{2}\right)}+E+\lambda^{2}} $$ is real, when it is purely imaginary and when it is complex (with imaginary part not ...
1
vote
1answer
101 views

Eliminate some temporaries from a set of equations

I have a long set of equations, mostly obtained by introducing physics related quantities which stand for some kind of temporary variables: ...
1
vote
0answers
175 views

Making simultaneous equation solving more efficient

I am trying to solve a system of several simultaneous equations that have been generated by a series of modules and functions, using this module: ...
0
votes
0answers
180 views

Select and plot real positive solutions for a sixth order parametric equation

I need your help in order to solve the following problem: I have a sixth order equation: $ax^6+bx^5+cx^4+dx^3+ex^2+fx+g=0$ and I solved it using Solve[] command, ...
1
vote
1answer
220 views

Equating and solving equations that have been generated using table[]

I am in the process of trying to use Mathematica to find the coefficients of transmission and reflection for the wavefunction of a beam of particles tunnelling across any number of identical potential ...
2
votes
1answer
90 views

Possible to Solve a LocationEquivalenceTest?

I have 5 groups, each containing around 20 elements. These elements are all dependent on x. For example: Set1 = {1.5x + 1, 2x + 0.5, 1 x + 1, ...} etc. Now, I want ...
8
votes
1answer
406 views

Complex valued 2+1D nonlinear PDE using NDSolve

I am trying to follow the main ideas presented in this question, applying it to my own problem, which is a complex, time-dependent, nonlinear PDE: $$i \frac{\partial \psi}{\partial t} = \left[ ...
4
votes
1answer
158 views

Check if an inequality holds among the solutions returned by Solve [duplicate]

Let's say I solve a system: Solve[{a == 3* c, b == 2 *a}, {a, b}] and then want to see if the values found for a and ...
1
vote
1answer
133 views

FindMinimum gives wrong solutions inside a loop

I have a density function $\rho(r,z)$ and I want to calculate the minimum distance $d_{min} = \sqrt{r^2 + z^2}$ from the center (0,0) in which $\rho$ becomes negative. The easiest way is to find where ...
-4
votes
1answer
351 views

Solving Det[matrix] == 0 with an 8 x 8 matrix [closed]

I want to solve the equation Det[matrix] == 0 which came from the consistency of solutions of a set of 8 equations. This matrix has two constants λ and μ and two variables $P$ and $q$. I want to get ...
0
votes
1answer
315 views

How to nest the output of FindRoot in a table of Derivative evaluations?

I am using ParametericNDSolveValue to numerically solve an ODE system, which I then use to find the definite integral of one of the variables in the solution for different values of a parameter. Here ...
3
votes
1answer
475 views

How to increase Maximum number of steps in any other functions except NDSolve?

I want to plot an output response from a state space model. I use StateResponse[] to calculate it and then plot it. When I run my code, I face this message: ...
5
votes
0answers
983 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 ...
1
vote
4answers
1k views

Solve trigonometric equation

I'm looking for a solution (graphic, numeric or analytic) for a function of the form: $$a^2\tanh(x)=\tan(ax),\quad a ≥ 1,\ x > 0$$ preferably using Mathematica. Any advice?
1
vote
4answers
279 views

Calculating difference ratios (Δβ/Δρ) from a data set

I am little bit confused about how to calculate δβ/δρ value if I have set of values like this. I have the values of β and ρ like this. ...
5
votes
2answers
327 views

Adding noise to nonlinear control system using NDSolve

I have a nonlinear control system ...
4
votes
2answers
456 views

Why doesn't FindRoot work correctly?

I'm trying to find the roots of the following equation: I need to find λs for different values of ξ. I know that for all ...
4
votes
1answer
720 views

What do the hashtags represent in the result of Solve, and how should I use them? [duplicate]

There is a function that I'm trying to get the inverse of. My function is a simple polynomial: Tn[T_] := 4/9 T^3/Tc^2 + 5/9 T Now I tried to find ...
0
votes
0answers
242 views

DSolve expression doesn't evaluate

Can Mathematica solve $\; d^2/dx^2{}+ (1/x) d/dx\;$ form of equations? For example, I am trying to solve the system of equations given below: ...
0
votes
0answers
94 views

Inconsistent results in fits from NArgMin

EDIT: Just realized I had misspelled "inconsistent." I'm using version 7.0. I'm trying to fit a (noisy) data set to a large-order polynomial. (Just for context: there isn't a model for the ...
1
vote
0answers
251 views

Why is a bump function making NDSolve take forever to solve?

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...
2
votes
1answer
195 views

Solving this system of equations produces an error message about badly conditioned matrix

I want to determine a balance distribution. Ü = {{0.4, 0.2, 0.3}, {0.3, 0.5, 0.2}, {0.3, 0.3, 0.5}}; and ...
2
votes
1answer
636 views

How to take the derivative w.r.t. an arbitrary function?

EDIT: The answer posted by @Jens works for built-in functions only. However I'm starting to wonder if this is related to my Mathematica install somehow. I have version 7. Here is an example in the ...
1
vote
1answer
282 views

Solution of Non-Linear Equations using Simulation

How I can solve these five non-liner equations where n=3, x=1,3,8 (e.g), and a,b,c, Alpha ...
3
votes
3answers
204 views

Solving $(-1-z)^n = z$, for $z$ in the unit circle

I want to solve the following equation: $$(-1-z)^n = z,\quad |z|<1,\quad n>1\in \mathbb{N}$$ where $z$ is a complex number. However Solve or ...
0
votes
1answer
572 views

Solving coupled eigenvalue differential equations

I am trying to solve an equation of the form as follows $\left(\begin{array}{cc} -\frac{\hbar^{2}}{2m}\frac{\delta^{2}}{\delta z^{2}}+\sin^{2}\left(z\right) & z\\ z & ...
3
votes
2answers
273 views
2
votes
1answer
674 views

How could I define a function as the solution of equations in Mathematica?

I have posed a specific question yesterday but it may be too trivial to answer. I think the question could be asked in a more general way so it is easier to answer. Then I could solve the original ...
6
votes
2answers
603 views

Solution of equation with power series (perturbation)

So I need to use Mathematica to find the solution of $y=x- \epsilon \sin(2y)$ as a power series in terms of $\epsilon$. I'd assume I'd need to create an equation $f=x-y- \epsilon \sin(2y)$, then ...
4
votes
1answer
1k 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 ...
2
votes
1answer
289 views

Problem with Sinc[x] function and rounding

I seem to be having some trouble with the Sinc[x] function, and I think it's due to rounding, but I'm not sure. The code is below, with relevant constants: ...
4
votes
0answers
148 views

Solving a nasty equation

Here's an equation that I need to solve for $t_k$ $$ \theta_0 = \tan^{-1}\left(\frac{2(w_x - m)}{p - g {t_k}^2 - 2 t_k w_y}\right) - {\frac{1} {r}} \left( \left(\frac{m}{t_k}\right)^2 + \left( ...
0
votes
0answers
56 views

NMinimize and FindRoot Issues with System of Equations [duplicate]

I am trying to solve a constrained optimization problem with a system of transcendental equations and am running into issues with NMinimize. I have a system of equations (...
6
votes
3answers
590 views

How do I find the intersection of a closed 3D curve given by numerical data with a specified plane?

I have a list of 3D data points which form a closed curve. My own data can't be easily generated analytically, but the qualitative behaviour is well represented by a parametric curve families such as ...