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

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0
votes
1answer
110 views

NSolve takes too long time!

I am trying to solve the following problem numerically and I faced two things: 1- It takes too long time to give solutions. 2- there are many roots for the equation but NSolve doesn't give all thee ...
0
votes
1answer
66 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 ...
2
votes
1answer
73 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: ...
0
votes
1answer
32 views

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

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: ...
13
votes
0answers
113 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
42 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 ...
2
votes
0answers
112 views

Why can't Mathematica solve this equation? [duplicate]

Possible Duplicate: Can Reduce *really* not solve for x here? Why can't Mathematica solve this equation? ...
3
votes
1answer
79 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 ...
0
votes
0answers
62 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
votes
0answers
56 views

Root of a cubic is not always real [on hold]

In my Mathematica output, the following root object occurs ...
0
votes
1answer
25 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 ...
10
votes
2answers
2k views

Error entering equation in DSolve

I entered a command incorrectly as follows: DSolve[{y'[x]=y[x]},y[x],x] I am now experiencing: ...
8
votes
3answers
163 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
140 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, ...
1
vote
3answers
229 views

Find all roots of a function with parabolic cylinder functions in a range of the variable

I want to find all roots of a function involving Parabolic Cylinder Functions. In what follows, I define 2 variables $\xi1$ and $\xi2$, which in turn depend on $\omega$. My function is then defined as ...
10
votes
1answer
185 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 ...
8
votes
3answers
913 views

Implement the Bisection algorithm elegantly and easily

Description: Rencently, I have finished my course Numerical Analysis, so I'd like to implement many algorithm that I have learned from that course.By this practice, I hope that I can improve my ...
2
votes
0answers
67 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 ...
1
vote
1answer
44 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?
0
votes
0answers
57 views
0
votes
0answers
42 views

NDSolve won't stop running [on hold]

I'm trying to solve the wave equation with NDSolve, but everytime I hit evaluate notebook it won't stop running. Any insights? ...
0
votes
1answer
76 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
0answers
33 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 ...
3
votes
2answers
299 views

Roots of Whittaker W function

I am interested in finding the roots $u$ of the equation $$ W_{1,\imath b}(a)=0, $$ where $W_{\kappa,\mu}(z)$ denotes the Whittaker $W$ function, $a>0$ is a fixed parameter, $\imath=\sqrt{-1}$ and ...
1
vote
3answers
122 views

NSolve or Solve or FindRoot

I need to solve this equation: A == M/(f d/2 (1 + Sqrt[1 - 3.53 (M/(b d^2 c))])) to find M, with: A = 0 to 19635 for intervals of 5 f = 500 d = 100 to 500 ...
5
votes
2answers
151 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 ...
1
vote
1answer
198 views

Solving wave PDE

I am trying to solve the wave PDE with NDSolve. Below is the equation: ...
0
votes
2answers
78 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, ...
0
votes
2answers
86 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
95 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: ...
-1
votes
0answers
74 views
7
votes
3answers
185 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} $. $\text{The estimate}$ $\# \{n \le x:n! \text{ is a sum of three squares}\}=7x/8+O(x^{2/3})$ ...
0
votes
2answers
66 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
138 views

Verifying the outputs of 'Solve'

I got a solution for the equation ...
10
votes
1answer
187 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
vote
1answer
79 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 ...
-5
votes
1answer
33 views

Getting SetDelayed::error from Solve [closed]

I defied three functions as following: f1 = a1 x1 +a2 x2 + a3 x3 f2 = b1 x1 +b2 x2 + b3 x3 f3 = c1 x1 +c2 x2 + c3 x3 and I wrote ...
-1
votes
1answer
39 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 ...
57
votes
9answers
3k views

Updating Wagon's FindAllCrossings2D[] function

Stan Wagon's Mathematica in Action (second edition; I haven't read the third edition and I'm hoping to eventually see it), demonstrates a nifty function called ...
1
vote
2answers
72 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: ...
3
votes
1answer
62 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
1answer
159 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. ...
0
votes
1answer
75 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 ...
0
votes
2answers
104 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 ...
2
votes
2answers
70 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 ...
0
votes
0answers
4 views

Finding multiples of three given a few simple rules [migrated]

We were given this problem the other day and it seems a little over my head, so I thought I'd share it here for any possible advice or assistance :). The problem is as follows: Initially, x = 1. For ...