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

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-2
votes
1answer
202 views

Symbolic Simulations

I have 9 nonlinear equations and 10 unknowns. It is not possible to obtain a numeric solution but I do get a parametric solution. It is useful in my case because I want to observe how parameters (p1, ...
3
votes
0answers
768 views

FindRoot gives a wrong solution which obviously should not be there

I got stuck on FindRoot and I didn't see any similar problem posted, so let me explain what I am trying to do and what problem I meet here. I try to find roots of a particular function, which in the ...
2
votes
0answers
154 views

Nest for large value of n

I am working on a problem to find the Feigenbaum constant. In this problem I have to get $f^{2^n}(1/2)$ with $f(x) = kx(1-x)$. I use Nest to get $f^{2^n}(1/2)$ but ...
2
votes
1answer
153 views

Solving a system of equations

Mathematica doesn't want to solve my exact system with 3 equations and 3 variables. ...
7
votes
0answers
591 views

Creating and using an explicit piecewise function in a convenient way [closed]

I have a set of data points that define a function in the form curvePts = {data1,data2,...} where ...
3
votes
1answer
653 views

A basic problem with Solve

I have this equation: 4b*Cos[2t]-4a*Sin[2t]==4Cos[2t]+8Sin[2t] Which I would like to solve. Without using mathematica, you can pretty easily see that a = -2 and ...
3
votes
2answers
257 views

Mathematica does not understand (R^3)^(1/3) is the same as R [closed]

In the output from a calculation in mathematica stands a/((R^3*c)^(1/3)), with c and a ...
2
votes
0answers
403 views

Conditional statements in intial conditions?

This is potentially a daft question, but I thought I'd ask it; I have some material free to diffuse in a boundary between rn and ro; I've been able to get it working nicely for neumann type boundary ...
13
votes
1answer
339 views

ToNumberField won't recognize Root as an explicit algebraic number

Bug fixed in 10.0.0 In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an ...
0
votes
1answer
223 views

solution of differential equation

I have the following code that gives you a phase portrait of a 2d system and I can't understand what means the 3rd and 4th line (sol1 and sol2). ...
0
votes
1answer
104 views

Define variable relationships and dynamically update variables

I would like to define a relationship between 3 variables first and then later when I have filled two of the variables with a number, I would like to extract the value of the last value. For example: ...
0
votes
1answer
203 views

How to delete duplicate solutions of this system of equations?

I want to find vertices (has integer coordinates) of the triangle $ABC$ with the centorid is $G(1,1)$ and orthocenter is $H(3,3)$. I tried ...
1
vote
1answer
594 views

Solving Intervals

In a recent question I posed, it was noted that by design, Sqrt[ blah] only returns the positive branch, even though we might want to obtain all possible symbolic solutions. So, taking care to avoid ...
6
votes
1answer
175 views

Why is FindInstance failing when I relax a set of constraints?

I'm attempting to use FindInstance to generate coordinate sets for plausible triangles with edge length distance constraints. E.g.: ...
4
votes
1answer
777 views

How to solve this equation with integers as a solution?

I want to solve the equation $$x^y + y = y^x + x$$ with $x$, $y$ are integer numbers. I tried Solve[x^y + y == y^x + x, {x, y}, Integers] How to solve the ...
5
votes
2answers
537 views

Using RSolve correctly

I am having problems persuading Mathematica to solve even the simplest recurrence relations. As an example, how would you do the following? ...
1
vote
2answers
3k views

Using FindRoot with an interpolating function

This question bears resemblance to a few other questions on mathematica.SE about finding points of intersection of crossing curves. I know that the guidebook of numerics has an entry about the whole ...
5
votes
3answers
813 views

Solving a system of equations with conditions related to the number of solutions

The equation below describes a conic with oblique axis: $$9 + 22 x + 9 x^2 + 46 y + 24 x y + 16 y^2=0$$ It is a parabola, as the coefficients in $x^2$, $y^2$, $xy$ form a perfect square. To find the ...
4
votes
1answer
165 views

Find point at which equation stops having roots (if it exists)

I am interested in the roots of this function: f[M_, b_] := 1 - (2 M Gamma[2, 0, (1/M + b M)/Sqrt[b]])/(1/M + b M) for fixed values of b. In particular I want ...
0
votes
0answers
244 views

Finding all roots of the system of two complex equations

I need to find all roots for the system of two complex equations. Obviously I can rewrite them as 4 real however problem remains. I have looked through routines connected with using ContourPlot ...
0
votes
1answer
112 views

Plotting query - same values on Y-axis / viewing data

I'm new to Mathematica, and have numerically solved two similar functions with the following code; ...
0
votes
1answer
356 views

Solving a system of equations using subscripted variables

I want to solve this equation: X(i, j) + C*Y(i, j) = Z(i, j) Where ...
0
votes
1answer
567 views

Upper bound for x

I want to ask a question about Reduce. I have a function, say f[x]. When I use the command ...
4
votes
1answer
528 views

Create Euler equation

I've tried to make some research, but without any luck. How do I setup the Euler equation for this in Mathematica?: $ \text{Min} \int_0^1\left(2x^2+ \left(4t-5 e^{r \, t} \right) x \, \dot{x} + 12e^{...
0
votes
1answer
241 views

Difference between FindInstance and NSolve

Assume that ...
2
votes
1answer
754 views

How to guess initial complex value for FindRoot

I have to solve a transcendental equation for a parameter, say $\beta$. Now, the $\beta$ has a range from $ik$ to $k$ where $i$ is the usual imaginary root $\sqrt{-1}$ and $k$ is a real number. ...
1
vote
0answers
67 views

Finding Maximum Root [duplicate]

How can I find the greatest root for a polynomial if the polynomial degree is very large. One way is using NSolve. This command can find all roots in numeric. Then, ...
5
votes
1answer
203 views

Find the domain in which a sequence converges

I seem to have a lot of problems in the format of: Given the sequence $a_n=\frac{n^\alpha+1}{2n^8+5}$, for $\alpha > 0$, find the values of $\alpha$ such that the sequence converges. However, ...
1
vote
2answers
329 views

Reduce on equations involving integrals

Here's part of problem from a college physics text: A time-dependent force F = (8.00 i - 4.00 t j) N (where t is in seconds) is applied to a 2.00-kg object initially at rest. (a) At what time ...
2
votes
0answers
485 views

differential equations with implicit functions

I have an ordinary differential equation that contains coefficient functions that depend implicitly on the independent variable via an algebraic equation. I am trying to go ahead and use NSolve to ...
1
vote
3answers
330 views

Find a single max value

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2
votes
1answer
126 views

InterpolatingFunction with growing Domain

I want to find roots of a function that is very slow to calculate (the function itself involves a bunch of FindMaxima) so I interpolate the function in a region where I think it likely the the root is,...
5
votes
2answers
315 views

Computing the sign of the real part of eigenvalues in a 3D linearized system with 3 parameters

So I have this dynamical system given by: $$ \left\{\begin{aligned} x' &= a(y-\phi(x))\\ y' &= x-y+z\\ z' &= -by \end{aligned}\right. $$ where $\phi(x) = \mu x^3 - \nu x$ and $a,b,\mu,\nu$ ...
3
votes
2answers
266 views

Computing the minimum distance in a contour plot

I have the following Mathematica code ...
4
votes
3answers
197 views

How do I generate a set of n-tuples containing integral solutions to a linear equation provided certain constraints?

Let $m,k,p$ be fixed positive integers. I want to create a table of k-tuples $(x_1,x_2,\ldots,x_k)$ comprised of solutions in positive integers to the equation below: $$x_1+x_2+\cdots+x_k=m\quad\...
2
votes
1answer
160 views

Differentiating with respect to vectors of unspecified length

Given a function defined by f[x_,y_] := Sum[ x[[i]] (g[y[[i]]] - g[Total[y]] - Log[x[[i]]]), {i, 1, Length[x]}] I can easily calculate the derivative for a fixed ...
1
vote
2answers
936 views

Rearranging an equation with the sine function in it [closed]

When I evaluate Solve[a==Sin[b*c], b] to rearrange the following for $ b $: $$ a = \sin(bc) $$ I get the following result from Mathematica: $$\begin{align*} \...
2
votes
2answers
434 views

A While Loop with two different steps/iteration

I'd like to know if there is a possibility to solve an equation in a while loop with 2 different steps. I want the step to be small at the beginning and bigger after a certain value of sigma (sigma is ...
5
votes
2answers
657 views

Extracting Reduce results

I'm solving a Diophantine equation inside of a function using Reduce but I'm having trouble extracting the necessary parts of the answer. For example, if my input ...
0
votes
1answer
1k views

Solving derivative of cumulative normal distribution log likelihood

I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of ...
2
votes
1answer
1k views

NDSolve two PDE plus one ODE, together

I have a couple of PDE (time and space/length) that are correctly managed by NDSolve, but to which I’m adding an ODE on which the acc “accumulates”, through time, a ...
2
votes
2answers
114 views

Puzzling behavior produced by Exists

I need to simplify a set of solutions of a system, say for example: ...
0
votes
1answer
280 views

Dynamic boundaries for FindRoot

As documented FindRoot[f[x], {x, xs, min, max}] searches for a solution, stopping the search if x ever gets outside the ...
3
votes
1answer
2k views

NDSolve does not respond

For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
0
votes
1answer
209 views

Solving a differential equation for a variable in a function

This may sound like a very trivial question, but I need to solve a differential equation as follows: ...
1
vote
1answer
673 views

Substituting solution from Solve into the equation and making a plot

I want to solve an equation and substitute it into a Plot expression. My code looks something like this a[b_, x_] := bx + 1; sol = Solve[(1 + b)x + 1 == 0, b] I ...
14
votes
3answers
6k views

Solving a time-dependent Schrödinger equation

I want to solve the time-dependent Schrödinger equation: $$ i\partial_t \psi(t) = H(t)\psi(t)$$ for matrix, time-dependent $H(t)$ and vector $\psi$. What is an efficient way of doing this so that ...
2
votes
1answer
173 views

Any solution to system of equations?

I need ANY combination of 8 variables which satisfy: a+b+c+d+e+f+g+h=0 a^2+b^2+c^2+d^2+e^2+f^2+g^2+h^2=1 a*b+b*c+c*d+d*e+e*f+f*g+g*h+a*h>2/3 Ideally these ...
7
votes
1answer
251 views

How to plot inequalities taking into account that points must be integers and not reals?

I have solved with Mathematica 9 the following integer inequalities using Reduce: ...
1
vote
1answer
261 views

Is my system too complicated for Solve?

I am trying to solve a system of three nonlinear equations using Mathematica. Solve takes forever to run and never solves my system of equations. Is my system too ...