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

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2answers
111 views

Find all the non-negative integer solutions of a linear equation

For the linear equation x[1] + x[2] + x[3] + x[4] + x[5] == n Is there any efficient way to find all the non-negative integer solutions of this equation when n ...
0
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1answer
56 views

Module output rules like Solve FindRoot etc built-in functions

How do I print rules {x -> values} as an output from my module? I'd like it formatted just like those from the built-in functions, so that users can use Out[ ] or % to directly apply the rules. ...
5
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0answers
48 views

Is there a way to tell how much time FindRoot is spending calculating Jacobians?

I am solving a large number of trascendental equations by scanning FindRoot over a bunch of seeds and a bunch of different parameter values, and I would like to ...
0
votes
1answer
68 views

Solution for Imaginary part of equation

I have a function Il12i[-0.001, -0.001, w, 0, 1, 0, 0.1002] which is depends on 1 variable w and it is real if w > -3666 (this number I found from graphs). This function is very complicated numerical ...
0
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0answers
28 views

Question about # Symbol [duplicate]

I am trying to solve an equation and the solution includes # symbols. I read up on them but can't understand how they are related to my solution. I solved a simple trigonometric equation of third ...
2
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1answer
63 views

Solving a big number of non linear equations

I have three trapezoids. The first sharing its upper side (I will call b_{i+1} in the code) with the second, the third sharing its lower side with the upper side of the second. All shared sides are ...
0
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0answers
34 views

How to speed up Solve command in Mathematica 8.0?

I have two complicated mathematical functions $f(s)$ and $g(M)$ that are complicated functions of $s$ and $M$ respectively. I would like to solve the equation $f(s)=g(M)$ in order to plot $s$ vs. $M$. ...
0
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1answer
54 views

Solving equations with change of variables is not working?

I have the following expression $$\text{expr=}\int_0^{\infty}\frac{C\exp(-\frac{mx^2}{\Omega})}{\Omega^m}\frac{1}{\sqrt{2\pi}\lambda\Omega}\exp\left(-\frac{(\ln ...
0
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2answers
64 views

Unable to plot function with exponentials or to find all roots [duplicate]

I am not able to Plot[(-1)^x + 2^x - 2 x - 1, {x, -4, 4}] directly. Some rework might be needed with complex branch cuts perhaps. There are real roots at $ x=3, ...
3
votes
1answer
220 views

Is there a package to find ALL exact roots of a polynomial, if they exist?

There are polynomials with roots not expressible with radicals but expressible as trigonometric or other functions, for which Solve[] only returns ...
0
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1answer
37 views

Why do I not get a result when there is no error message? [closed]

I've typed in the following equation: Solve[((h*s + l - r*s - r)/(s^2 + s)) (1 + s) - h == (h*s + l - r*s - r)/(s^2 + s) - r, r] and it produces: ...
18
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1answer
255 views

Can Mathematica solve functional equations with nested variable?

First, inline free form input can solve these equations: But it seems no native Mathematica function can solve these, there is even an error page for equations of this form (nestdv). Now my ...
3
votes
1answer
50 views

How can I choose the coeffcients so that the givent system of equations has four integer solutions?

Consider the system of equations with unknown are $(x,y)$. $$\begin{cases} a_1x^2+b_1y^2 + c_1xy+d_1x + e_1y+f_1=0,\\ a_2x^2+b_2y^2 + c_2xy+d_2x + e_2y+f_2=0. \end{cases}$$ I want to find the ...
1
vote
1answer
70 views

Finding roots of Bessel function $y=3J_1(x)+xJ_1'(x)$ is returning inaccurate roots. Not Kernel bug [closed]

I can't figure out why Mathematica is returning the incorrect roots. The first five should be 2.9496,5.84113,8.87273,11,9561, and 15.0624 according to my textbook. ...
3
votes
1answer
84 views

How to efficiently find only the rational roots of a rational complex polynomial?

I need to find all the rational roots of a bunch of high-order polynomials with rational complex coefficients. Is there an efficient way to do this? My best effort on an example polynomial: ...
4
votes
1answer
99 views

Does Solve[] find ALL the exact roots of rational polynomials?

Does Solve[] find ALL the exact roots of rational polynomials? I've done a bunch of tests where I created an expression with some analytic roots, and Solve[] always found them all. But is the ...
1
vote
1answer
232 views

Why Integral does not converge?

I am trying to solve for $\Omega$ this nonlinear integral equation: $$1+\dfrac{z}{k^2}-\dfrac{z^2}{K_2(z)} \dfrac{\Omega}{k^3} \displaystyle\int_{1}^{\infty} \gamma^2\, \text{ArcTanh} ...
0
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1answer
37 views

Find a independent variable value from the numerical solutions of a system of differential equations

I have calculated the solutions for the following system of differential equations using NDSolve ...
12
votes
3answers
278 views

Archimedes' Scheme to find $\pi$

Given an Archimedes' scheme $$a_{n+1}=\frac{2a_nb_n}{a_n+b_n}$$ $$b_{n+1}=\sqrt{a_{n+1}b_n}$$ with initial values $a_0=2\sqrt{3},b_0=3.$ How do I prove using Mathematica that this converges to ...
1
vote
1answer
150 views

How do you solve a linear equation of matrices? [duplicate]

The function Solve works fine for scalars: In[]:= Solve[A x - x B + C == 0, x] Out[]= {{x -> -(C/(A - B))}} When using matrices however, ...
2
votes
0answers
72 views

Complicated implicit plotting - can it be tackled?

I'm quite new to Mathematica and have already spent tons of time on problems of this type, browsing through tutorials and topics here. I'm now coming to conclusion that it cannot be done and am about ...
11
votes
1answer
219 views

NDEigensystem returns incorrect eigenvalues for 2D coulomb problem, eigenfunctions contain discontinuity

I posted a similar question a short time ago regarding the 3D Coulomb problem. Jens' excellent answer to this thread allowed me to obtain the correct eigenvalues and eigenenergies for that system. I ...
1
vote
1answer
46 views

NRoots Results: From Equations to List of Root Values [closed]

When I use Roots/NRoots, I get a disjunction of conditions as result. The conditions are normally of the type x == value How can I convert this to the list of root values?
2
votes
2answers
66 views

How to find intersection points of linear and semi-logarithmic plots

Hopefully the title depicts what I am trying to do. Below is a figure of my calculations that is shown in logarithmic scale in the x-axis. I am trying to find a way to find the intersection point at ...
0
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0answers
36 views

Recycle boundary condition

I'm having the following issue that can not find a solution , by using this boundary condition u[0, t] == 2 u[1, t] that Mathematica does not understand, someone ...
0
votes
1answer
78 views

How to find roots using the bisection method [duplicate]

First I plot the function and then I try to find a domain such that I can see the curve cut through the x-axis. I do this via trial and error ...
0
votes
2answers
82 views

Free-fall air resistance problem

I´m working on a free fall problem and I got an equation with variable $k$ when the situation has air resistance. Then I compared with no air resistance equation ($-4.9$, considering t variable). So, ...
6
votes
2answers
166 views

NSolve behaving differently in V9, V10.3 and V10.4

EDIT In a very fast response from Wolfram they state that this is a known problem and give an example of it working for version 10.4.1. $Version "10.4.1 for Microsoft Windows (64-bit) (April ...
0
votes
2answers
89 views

I'm trying to solve a system of complex equations

I'm simply trying to solve a system of equations and mathematica can't do it for all values over the region of interest. I have a 3x3 matrix that has a specific parametrization and after squaring the ...
1
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2answers
97 views

NSolve won't act on very large powers

I noticed that NSolve isn't running properly when I have some seemingly harmless numbers in my expression. Here is a simple example: ...
0
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2answers
70 views

FindInstance function

I have a question concerning the FindInstance function. If I write FindInstance[c == 3, {c, l}] I obtain {{c -> 3, l -> 33/10 + (8 I)/5}} Is there any ...
4
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1answer
141 views

Verifying the outputs of 'Solve'

I got a solution for the equation ...
10
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1answer
205 views

NDEigensystem cannot solve numerically the 3D Coulomb problem, while DSolve returns the right answer

After having derived by hand the eigenvalues and eigenfunctions for the 3D and 2D hydrogen atom, I want to solve the systems numerically using Mathematica. I need to do this because my next step is to ...
-1
votes
1answer
40 views

Solve returns empty list on system of 62 linear equations with undeclared known variables

Context: I am trying to solve a set of equations generated by hand from a complicated, but not particularly strange system via Newton's Second and Third Laws, and a few constraints. All the resulting ...
7
votes
3answers
203 views

Find the number of $n$ such that $n!$ is a sum of three squares

I want to check the following theorem by using Mathematica: $\textbf{Theorem} $. $\text{The estimate}$ $\# \{n \le x:n! \text{ is a sum of three squares}\}=7x/8+O(x^{2/3})$ ...
3
votes
1answer
64 views

FindInstance only satisfies half of my double inequality

FindInstance[ 298973528525.436 < 10^10*(n - k*3.32192809488736) < 298973528539.862, {n, k}, Integers ] Result is: ...
0
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0answers
25 views

How to select one solution of a system? [duplicate]

The system, Solve[{F[x,y]==0,G[x,y]==0},{x,y}] has to solutions {{x->x0,y->y0}} How can I choose, for example, ...
1
vote
2answers
78 views

how to find sum of variable c1+c2+c3 for expression combinations

how to find sum of variable c1 + c2 + c3 for expression combinations: ...
1
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1answer
214 views

Solving wave PDE

I am trying to solve the wave PDE with NDSolve. Below is the equation: ...
1
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1answer
81 views

Solve does not seem to work for this equation

I need to solve the following equation, for which I am using Solve as below ...
2
votes
2answers
73 views

How to Count the number of roots in the Domain from an equation

How do i Count[] the number of roots in the Domain and printout the intervals in x containing these roots. Given the function ...
1
vote
1answer
165 views

Why timing of FindRoot is almost the same even if the function is speedup significantly

This question is almost the same issue as this one. However, it seems that it didn't draw enough attention. Now I encountered the same problem. I previously make this post, I will copy the code here. ...
1
vote
2answers
342 views

Solving pure functions

I've been trying to use Solve with pure functions to receive function efinition and then use it with Map , to obtain results from mapping function to some data. Here is example ...
2
votes
1answer
47 views

best way for finding approximate root of monotonic sawtooth like function

First I will generate such kind of monotonic sawtooth like function called func ...
0
votes
1answer
36 views

How can I set a solution of NSolve into the variable [duplicate]

I am trying to solve an equation such as: NSolve[Integrate[G[x], {x, -∞, ∞}] == 1 && B > 0, B] when ...
1
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0answers
57 views

Reduce function with simultaneous equations and inequalities

I have some simultaneous equations that I want to solve, preferably analytically, yet I am unsure if the Reduce function is the correct route as it doesn't seem to ...
0
votes
1answer
76 views

How to plot a solution set? [duplicate]

I have two functions, let's call them $F1$ and $F2$. Both take the same three arguments: $x1, x2$ and $\epsilon$. With every $\epsilon^* \in [0,1]$, there should be either zero or one unique point ...
1
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1answer
89 views

Solve the interpolating function

I would have asked how to obtain the x given the y in an interpolating function, and I found the answer from here. But another question raised. I was dealing with measurement of the spectral ...
1
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2answers
41 views

how do I find the unknown coefficients of coupled equations

How do I find the unknown constants $x, y, z$ interms of a and b, using Mathematica. \begin{equation} \begin{split} 1&=-x+y+z \\ ...