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
40 views

Create a loop for assignment of Solve output [duplicate]

Is there a way to automatically assign the output of solve to a number of symbols? For example, assume that I have the solve statement as follows: ...
0
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0answers
52 views

The ` in Solve results [duplicate]

I assign the result of a Solve to the variable eq8. Then I attempt to use this result in the definition of a function as follows: ...
2
votes
2answers
53 views

Difficulty finding roots of an interpolation function from NDSolve

I have been trying to find the point at which one of the solutions of a system of two ODEs crosses zero. I used the method suggested in this answer to a previous question, which seemed to be the most ...
4
votes
1answer
91 views

Trying to create an interactive plot (newbie here)

I'm new at Mathematica so please bear with me. I am trying to create an interactive plot that will end up looking like this: I want to input values for certain variables and then plot a curve. This ...
1
vote
1answer
45 views

How to define a Reduce function in order to define two parameters afterwards

I'm trying to evaluate numerically an equilibrium for a system of ODEs: dA = c A + b B - a A dB = d B + a A - b B So I define a list of known parameters: ...
3
votes
1answer
64 views

Solve with Reals gives different answer

I'm very new to Mathematica (started using ver 10.4) and I was just verifying my calculations. I have the following equation: ...
-1
votes
1answer
192 views

Can Mathematica solve this integral numerically?

I need to evaluate numerically the following $$\int_0^{\infty}\exp\left(-\pi\lambda\mathbb{E}_H\left(\int_r^\infty\left(1-\exp\left(-sP_{\text{M}}Hr^{-1/\delta}\right)\right){\rm{d}}r\right)\right)2\...
1
vote
1answer
59 views

Testing equivalence of analytical expressions like $x^2 -x == x(x-1)$

On occasion I have two expressions that I may be equal but simplified differently, and I want to check if they are actually equivalent. Using the equation in the title, $x^2 -x == x(x-1)$, sometimes ...
0
votes
2answers
52 views

Solving several inequalities in Mathematica

I am a very beginner of Mathematica and the following will probably be a very stupid question. I have a bunch of inequalities in 6 unknowns and I want to find the set of values satisfying them. Can I ...
0
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2answers
76 views

FindInstance is very slow on an apparently simple problem

I wish to use FindInstance to find a set of solutions of this problem: ...
0
votes
1answer
49 views

Errors only when code is iterated

Hello I'm trying to have two for loops sweep two parameters and for each 2-tuple of those parameters I want to solve a differential equation. To do this I have the following code: ...
6
votes
2answers
274 views

Find a condition that b must satisfy so that Ax=b has solution

I'm new to Mathematica, so I'm sorry if this is really simple. I am trying to find the condition that vector b must satisfy so that Ax=b has solution. I would like to learn a general method, but I'll ...
4
votes
4answers
185 views

Solving Recurrence Equation $a_{n+1}=a_n(1-a_n)$

How to solve following recurrence equation $$a_0=2$$ $$a_{n+1}=a_n(1-a_n)$$ I tried: ...
0
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0answers
30 views

Finding results using qualifiers?

I have set of recursive function definitions and assumptions $\forall n.t1(n+1)=t1(n)-Y*S(n)$ $\forall n.t2(n+1)=t2(n)+S(n)$ and assumption $\forall n.n<K\rightarrow L1=L2*t2(n)+t1(n)$ I want ...
0
votes
1answer
53 views

Reduce unable to solve simple inequalities with quantifiers

I have try to solve following inequalities using Mamthematica. But it unable to solve that. ...
2
votes
1answer
55 views

Substituting values of variables in solution of a system of linear equations

After solving a system of 21 linear equations in 21 variables (called Xi in my code) I got the values for all the 21 variables, in the following way: ...
2
votes
1answer
44 views

Help Compiling Vectors using Iterations

So I have a nice code that runs properly, which I include below but, in my naiveté, I'm having issues iterating my procedure. Simply put, I have a function of two real variables $f(x,y)$ and I want ...
3
votes
1answer
81 views

Solve equation for a function as solution

I need to solve the following function: $$ h(z) = \sum^{40}_{k=0} \frac{k \, p(k)}{z- k \, h(z)} $$ where $p(k)$ is a probability distribution (in this case binomial with n = 40). Note that $h(z)$ is ...
1
vote
1answer
78 views

Solving two equations with modified Bessel functions

I am trying to solve two equations with Bessel functions in them, 1) C1*BesselK[0, 3.7268*10^-4*x] == 1.3*10^-6 2) ...
0
votes
1answer
36 views

Parameterize Subset of Complicated Zero Set

I recently asked this question: Evaluating Functions on Zero Sets (of other functions), and got fantastic assistance, but realized that there seems to be an extra issue when you're trying to ...
0
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0answers
26 views

Using the “reduce” function with s lot of equations and inequalities

I am using "reduce" to obtain all positive integers (plus 0) which satisfy a group of equations and inequalities. I have to automatize this procedure because I have to use "reduce" with at least 100 ...
0
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0answers
38 views

Matrix with equations as entries - how to choose them and solve them

I have a matrix in Mathematica, which I have built using Normal[SparseArray]. Each entry of this matrix is an equation in one variable. What I need to do is 1) to select some of the entries of the ...
0
votes
1answer
56 views

Arranging sides of an equation [duplicate]

I have to create my own function to solve equations (first and second degree). Assuming you have any input equation, how can I do to bring everything to the first side of the equation? Example. I ...
3
votes
2answers
108 views

Evaluating Functions on Zero Sets (of other functions)

I have a highly non-trivial function, call it $f(x,y)$, in which I want to look at its zero set in the $(x,y)$ plane, and plot/evaluate a different function $g$ precisely along this zero set. I have ...
1
vote
2answers
130 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
votes
1answer
76 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
51 views

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

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
71 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
votes
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
votes
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
36 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
votes
1answer
72 views

Solving equations with change of variables is not working?

I want to express it in the form $$\text{expr=}\int_{-\infty}^{\infty}C_1\exp\left(-t^2\right)f(t)dt$$, i.e., the integrand is a bounded smooth function $f(t)$ times $\exp(-t^2)$ and the domain of ...
0
votes
2answers
66 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
227 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
38 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: ...
19
votes
1answer
306 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
57 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
81 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
94 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
107 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
241 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
62 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
292 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
155 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
78 views
2
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1answer
109 views

Complicated implicit plotting [closed]

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
250 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
70 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 ...