Tagged Questions

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

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4
votes
2answers
268 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
407 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
390 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
473 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: ...
2
votes
2answers
344 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
521 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
362 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
811 views

Error/warning when using NSolve for simple equation

I am using NSolve to solve an equation, as shown here: ...
2
votes
1answer
120 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
188 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
415 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
133 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
135 views

Solving a system of equations

Mathematica doesn't want to solve my exact system with 3 equations and 3 variables. ...
7
votes
0answers
426 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
225 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
245 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
280 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
217 views

Simultaneous Equation Solving Under Nonnegative and Bounding Conditions

I have nonlinear equations to solve parametrically; ...
12
votes
1answer
247 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
190 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
93 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
109 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
313 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
150 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
464 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
269 views

DSolve::overdet for system of linear PDEs

I would like to resolve symbolically the following equation: ...
5
votes
2answers
307 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
185 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
415 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
117 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
186 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
250 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
416 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
309 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
154 views

Difference between FindInstance and NSolve

Assume that ...
1
vote
1answer
344 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
142 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
221 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
304 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
293 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
252 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
240 views

Computing the minimum distance in a contour plot

I have the following Mathematica code ...
2
votes
2answers
120 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
127 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
373 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
251 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 ...