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

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3
votes
0answers
539 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
136 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
140 views

Solving a system of equations

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

Creating and using an explicit piecewise function in a convenient way

I have a set of data points that define a function in the form curvePts = {data1,data2,...} where ...
2
votes
1answer
288 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
252 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
314 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 ...
0
votes
0answers
260 views

Simultaneous Equation Solving Under Nonnegative and Bounding Conditions

I have nonlinear equations to solve parametrically; ...
12
votes
1answer
275 views

ToNumberField won't recognize Root as an explicit algebraic number

In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an explicit algebraic number. ...
0
votes
1answer
206 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
96 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
134 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
365 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
160 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
528 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 ...
0
votes
0answers
346 views

DSolve::overdet for system of linear PDEs

I would like to resolve symbolically the following equation: ...
5
votes
2answers
359 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? ...
0
votes
0answers
232 views

Defining and Solving Systems of Equations Using Matrix Tables

I've defined a system of equations, but I been unable to get Mathematica to solve for the individual variables created by matrix tables. ...
1
vote
2answers
2k 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
605 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 ...
3
votes
1answer
126 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
208 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
103 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
283 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
454 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
344 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} + ...
0
votes
1answer
167 views

Difference between FindInstance and NSolve

Assume that ...
1
vote
1answer
451 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
65 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
162 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, ...
0
votes
2answers
243 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
350 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
307 views

Find a single max value

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2
votes
1answer
115 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 ...
5
votes
2answers
273 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
250 views

Computing the minimum distance in a contour plot

I have the following Mathematica code ...
3
votes
2answers
141 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: ...
2
votes
1answer
137 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
508 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
297 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 ...
4
votes
2answers
391 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
903 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
107 views

Puzzling behavior produced by Exists

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

DSolve fails to solve second order PDE

I have a very simple example of a second order PDE: eqn = D[u[x, y], x, y] + u[x, y] == 0; sol = DSolve[eqn, u, {x, y}] and Mathematica cannot solve it! What is ...
0
votes
1answer
231 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
1k 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
185 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
434 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 ...
11
votes
3answers
4k views

Solving a time-dependent Schroedinger equation

I want to solve the time-dependent Schroedinger 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 ...