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

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9
votes
1answer
265 views

Efficient way to solve equal sums $x_1^k+x_2^k+\dots+x_5^k=y_1^k+y_2^k+\dots+y_5^k$ with Mathematica?

I need to solve the system of equations, call it $S_1$, in the integers $$x_1x_2x_3x_4x_5 = y_1y_2y_3y_4y_5$$ $$x_1^k+x_2^k+\dots+x_5^k=y_1^k+y_2^k+\dots+y_5^k,\;\; k= 2,4,6$$ I used a very ...
3
votes
2answers
178 views

Bounds on random number

I have a Markov Chain Monte Carlo code that uses a chi squared function to fit some data. I am running into an issue now with getting unrealistic values for some of the free parameters in the code. ...
17
votes
1answer
1k views

The Orbit and Perigee of the Flamsteed comet

Historical context This year we have the 330-th anniversary of the Battle of Vienna - one of the great formative events of European history, it took place on September 12, 1683. Kara Mustafa, Grand ...
5
votes
2answers
373 views

Reducing exponential inequalities fails

I am quite stumped by this problem : Reduce[ N^(x-y) <1 && N > 0 , x, Reals] gives the expected result ...
4
votes
2answers
264 views

find where 3 inequalities are simultaneously greater than zero

I have 3 functions: f11[l], f12[l] and f13[l], and I would like to know for which values of ...
1
vote
1answer
336 views

Prandtl-Meyer function

I'm trying to solve for Mach number based on the given Prandtl-Meyer function, however I keep getting odd error. Here is my code: ...
2
votes
0answers
351 views

I can't solve this set of equations

I am having trouble solving a set of equations in mathematica. I do not get any errors, but i don't get any answers as well. I have some restrictions on my parameters and variables in the equations ...
5
votes
3answers
454 views

Solve for the intersection point of 3 surfaces

Basically, I have three 2-torus (tilted) in 3-dimensional Euclidean space. They are expressed by parametric equations: ...
1
vote
2answers
331 views

Count and plot the number of solutions in an interval

I have equations depending on one or more parameters and I want to find and plot regions in the parameter space in which there is a specific number of solutions. For definiteness let's consider a ...
1
vote
1answer
494 views

solving a cubic equation

I need to find the minimum $r$ and the maximum $k$ of the following cubic equation for which there does not exist three distinct real roots. $rx^3-rkx^2+(r+k)x-rk=0$. Is it possible to find such $r$ ...
0
votes
0answers
342 views

Solve equations real and imaginary part separately

For my system of equations, the procedure described in Solving complex equations of using Reduce works no more. How can I separate the real and imaginary part of ...
2
votes
1answer
711 views

Error/warning when using NSolve for simple equation

I am using NSolve to solve an equation, as shown here: ...
2
votes
1answer
118 views

Finding the root of a nested function with small values

I have reduced an error in my program to this line of code: FindRoot[Nest[# (1 - #) k &, 1/2, 2^4] - 1/2, {k, 3.5}] It works for $2^1, 2^2, 2^3, 2^4,$ but ...
-2
votes
1answer
186 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
389 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
132 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
131 views

Solving a system of equations

Mathematica doesn't want to solve my exact system with 3 equations and 3 variables. ...
7
votes
0answers
414 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
202 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
244 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
268 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
203 views

Simultaneous Equation Solving Under Nonnegative and Bounding Conditions

I have nonlinear equations to solve parametrically; ...
12
votes
1answer
240 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
185 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
91 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
102 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
299 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
146 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
447 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
252 views

DSolve::overdet for system of linear PDEs

I would like to resolve symbolically the following equation: ...
5
votes
2answers
295 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
174 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
1k 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
380 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
114 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
183 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
97 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
240 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
394 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 ...
3
votes
1answer
299 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
152 views

Difference between FindInstance and NSolve

Assume that ...
1
vote
1answer
320 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
61 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
138 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
208 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
280 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
290 views

Find a single max value

...
2
votes
1answer
108 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
248 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
239 views

Computing the minimum distance in a contour plot

I have the following Mathematica code ...