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

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20
votes
1answer
298 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
51 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
78 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
91 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
104 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
239 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} \left(\sqrt{\...
0
votes
1answer
55 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
287 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
154 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, ...
3
votes
1answer
76 views
2
votes
0answers
75 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
241 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
votes
0answers
38 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
88 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
169 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
91 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
vote
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
votes
2answers
72 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
votes
1answer
141 views

Verifying the outputs of 'Solve'

I got a solution for the equation ...
10
votes
1answer
225 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
42 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
211 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} $. $\text{The estimate}$ $\# \{n \le x:n! \text{ is a sum of three squares}\}=7x/8+O(x^{2/3})$ $\text{holds.}...
3
votes
1answer
67 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
votes
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
81 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
vote
1answer
216 views

Solving wave PDE

I am trying to solve the wave PDE with NDSolve. Below is the equation: ...
1
vote
1answer
85 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
168 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
50 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
vote
0answers
58 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
80 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
vote
1answer
91 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
vote
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 \\ 0&=y\frac{-4a}{b-\sqrt{b^2+8a^2}}+z\frac{-4a}{b+\sqrt{b^2+8a^2}...
0
votes
1answer
39 views

Expanding in terms of a function in Solve

I am almost sure Mathematica has a way to do what I am looking for. I am trying to fit a quadratic T(x) = ax^2 + bx + c to three values of the function analytically. I proceed as follows: ...
0
votes
2answers
58 views

Using result of Solve as plot parameter [closed]

Recently I have faced a problem I would appreciate it, if you helped me I have the following code in Mathematica I want to plot a function let say z * 10 * t where <...
0
votes
1answer
68 views

Solve equation in a interval

I have a particle bouncing in a rigid box, my code is this: ...
0
votes
2answers
110 views

Solve implicit system of equations

Hello everybody I try to solve this system of functions and try to plot it: x == 0.5(1.+Tanh[0.5*(x*y^2-eps1)/t] y == Tanh[(x^2*y+eps2)/t] with eps1 = 0. and ...
0
votes
0answers
43 views

Impose conditions on differential equations

This is my first post in Mathematica Stack Exchange, so thanks for your help and sorry for any rookie mistakes. I am solving the Einstein equations for two vectorial pertubations h_Alpha and v_Alpha ...
1
vote
1answer
40 views

“MemoryAllocationFailure” in DSolve

Mathematica 10.4, Windows 10, 6 GB RAM, 64 bits When I trying to solve DSolve[{v'[t] == 100 - 0.15 v[t]^2, v[0] == 30}, v[t], t] I get ...
4
votes
3answers
212 views

Solving equation

How can I solve this equation: ((a^2 - 1)*((a^2 - 1)*ArcTanh[a] - a))/(2*Sqrt[2*(a^2 - 1)^4]) == C*x I am looking a solution for $a$ in function of $x$. I tried <...
2
votes
1answer
106 views

Maximize a variable in NSolve Function

I want to solve a set of trigometric coupled equations with the NSolve funcion while at the same time trying to maximize a variable which has to be real and between ...
3
votes
3answers
183 views

Cantor Pairing Function

I'm inspecting the Cantor pairing function, that we can find on this link here. But the strange thing is that Mathematica is outputting a wrong result to me. The code below shows the strange behavior....
0
votes
0answers
39 views

Using previous outputs and equations for 3d plots

I am extremely new to Mathematica, and am trying to obtain some plots for my research work. I need to find the roots of a polynomial, and using the roots individually, I need to obtain another ...