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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0answers
46 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 ...
10
votes
4answers
436 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
184 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
125 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
396 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
84 views

Changing ParametricNDSolveValue options for only part of the run

Here is an example of the system that I am running, ...
0
votes
2answers
133 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
86 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 ...
0
votes
0answers
102 views

reduce taking too much memory

I have five integer variables j, k, i, nu, ...
1
vote
1answer
95 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
107 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
156 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
191 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 ...
0
votes
0answers
117 views

How to pass Jacobian to IDA via NDSolve

According to the IDA manual, when solving DAEs, there is an option to supply $J = df/dx + c*df/dx'$ (where $d$ is for partial derivatives) to the IDA module. How can I do the same via ...
2
votes
1answer
79 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
319 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[ ...
3
votes
1answer
117 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 ...
0
votes
1answer
181 views

Why the dollar signs when I Solve inside a Module [closed]

I would like the solutions of my equations to be local only, so I did a Solve inside a Module: Module[{a, b, c}, Solve[{a == 3* c, b == 2 *a}, {a, b}]] and the ...
0
votes
1answer
111 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
263 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 ...
-3
votes
3answers
189 views

How can I get a result with 12 digits of precision? [closed]

I tried to get a solution with 12 digits of precision using N[_,12] and WorkingPrecision -> 12. However all my trials failed. ...
0
votes
1answer
173 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 ...
0
votes
0answers
81 views

Is there a way to generalize FindAllCrossings3D to higher dimensions?

I understand the obvious visualization issues, but is there a way to extend the argument to higher dimensions, ie more equations?
3
votes
1answer
249 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: ...
4
votes
0answers
652 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
727 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
242 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
245 views

Adding noise to nonlinear control system using NDSolve

I have a nonlinear control system ...
4
votes
2answers
337 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 ...
3
votes
1answer
344 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
201 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
88 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
197 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 ...
1
vote
1answer
126 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
394 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
206 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
188 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
0answers
403 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
269 views
2
votes
1answer
480 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 ...
4
votes
2answers
346 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 ...
2
votes
1answer
717 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
207 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
120 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
53 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 (...
5
votes
3answers
400 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 ...
4
votes
1answer
196 views

How to add equations' left and right sides together?

If we have two equations E1 and E2, and instead of using Solve to solve it, we simply need to manually add them up which would allow some simplification that could ...
2
votes
0answers
160 views

Problems with Simultaneous Equation Solving

Let me first explain what I am doing and then I will explain the problem that I can't figure out. I am basically trying to solve 2 equations for 2 unknowns (a1 and ...
6
votes
2answers
871 views

Finding y given x from an interpolating function

I would like to put a dot on the point of a curve that has a specific y value but I don't know the x value. A simple example of my code is ...
1
vote
1answer
118 views

Corrected: Solve[] cannot solve simple hyperbola equations?

Is Solve[] very inefficient in solving equations involving square roots? The input below attempts to find out the explicit expression of either x or y in terms of other variables {x|y, a, c}, and c ...