Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
0
votes
0answers
74 views
Simultaneous Equation Solving Under Nonnegative and Bounding Conditions
I have nonlinear equations to solve parametrically;
...
0
votes
1answer
122 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
47 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
36 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
...
5
votes
3answers
200 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 ...
1
vote
1answer
115 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 ...
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votes
0answers
48 views
DSolve::overdet for system of linear PDEs
I would like to resolve symbolically the following equation:
...
2
votes
2answers
195 views
How do I get the solutions of a cubic equation in trigonometric form?
I know $x^3-3 x+1=0$ has three roots that can be expressed in trigonometric form:
$\{2\sin(10^\circ),\,-2\cos(20^\circ),\,2\cos(40^\circ)\}$.
How can I get this result with Mathematica?
4
votes
2answers
130 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?
...
7
votes
4answers
435 views
Finding the roots of Hypergeometric1F1[]
I am trying to find the roots, λ, for this equation:
Hypergeometric1F1[1/4 (2 - λ /β), n + 1, β]
for certain ...
10
votes
6answers
2k views
About multi-root search in Mathematica for transcendental equations
I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range?
Perhaps ...
1
vote
2answers
109 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 ...
0
votes
0answers
73 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.
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6
votes
1answer
455 views
Handling failed FindRoot calls
I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit)
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3
votes
1answer
74 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 ...
7
votes
3answers
530 views
Finding the number of solutions to a diophantine equation
I want to count total number of the natural solutions (different from 0) of the equation $2x + 3y + z = 100$, but don't know how. How can I calculate it using Mathematica? I tried:
...
0
votes
0answers
50 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
63 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;
...
8
votes
0answers
322 views
Proving inequalities with Mathematica
Question summary: I would like to learn some tips and tricks on how to prove inequalities with Mathematica.
I'm studying various inequalities in triangle that have the form $R+ar + bs\geq 0$, where ...
0
votes
1answer
94 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
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8
votes
3answers
398 views
Using FindInstance to Prove No Solutions Exist
For a small amount of background, I am currently working on an undergraduate research project in Combinatorial Geometry and I'm working on a case analysis for embedding spherical simplicial ...
12
votes
2answers
430 views
How do I split up a curve into segments of equal length?
I have a curve that is defined as f[x] and what I'm attempting to do is to divide the curve into equal straight lengths for a number of segments of my choosing that I've defined as nSeg.
I've created ...
3
votes
1answer
171 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} + ...
4
votes
3answers
223 views
How to solve this system of equations?
I want to solve the following system of equations:
$$\begin{cases}
1+\sqrt{2 x+y+1}=4 (2
x+y)^2+\sqrt{6 x+3 y},\\
(x+1) \sqrt{2 x^2-x+4}+8 x^2+4
x y=4.
\end{cases}$$
I tried
...
0
votes
1answer
79 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. ...
0
votes
1answer
62 views
1
vote
0answers
48 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
89 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
0answers
109 views
How to find the couple $a$ and $b$ of the equation? [closed]
I want to find the integers numbers $a$, $b$, $k$ of the equation
Sqrt[2 x + a] + Sqrt[b - 2 x] == k
so that the given equation has two reals solution.
I ...
7
votes
2answers
227 views
Finding all points of period n in an iterated map
I'm trying to implement an algorithm of Jenkinson and Pollicott to calculate the Hausdorff dimension of a Julia set for the map $f_c : z\mapsto z^2 + c$. It's described on page 40 of their paper, ...
1
vote
3answers
191 views
0
votes
2answers
70 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 ...
0
votes
3answers
75 views
Help solving a system [closed]
I am trying to solve this system for r and c but I get an error "Solve::ivar: r is not a valid variable.".
What is wrong here?
...
2
votes
0answers
88 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 ...
2
votes
1answer
77 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 ...
1
vote
1answer
142 views
Remove failed Solve[] attempts
I can't figure how to replace a failed evaluation with a null value.
I am very new to Mathematica.
I have an equation that are being processed using the Solve[] ...
2
votes
1answer
100 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 $a,b,\mu,\nu$ ...
2
votes
2answers
114 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 ...
3
votes
2answers
134 views
2
votes
2answers
59 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
175 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
1answer
55 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
81 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:
$$\begin{align*} ...
3
votes
2answers
81 views
Extracting Reduce results
I'm solving a Diophantine equation inside of a function using Reduce but I'm having trouble extracting the necessary parts of the answer.
For example, if my input ...
0
votes
1answer
219 views
Solving derivative of cumulative normal distribution log likelihood
I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of ...
3
votes
1answer
445 views
Solve pair of recurrence relations
[Corrected equations and added simple example]
Can you solve a system of (loosely) coupled recurrence relations like this in Mathematica somehow?
...
7
votes
3answers
293 views
NDSolve and {C, K, Slot} and other built-ins as a variable name
The following problem is an exploration of what causes the error "Input is not an ordinary differential equation" in Mathematica as it seems to have changed from version 8 to version 9.
Specifically ...
4
votes
1answer
172 views
NDSolve does not respond
For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
4
votes
2answers
508 views
Solving a time-dependent Schroedinger equation
I want to solve the time-dependent Schroedinger equation:
$$
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 ...
2
votes
2answers
90 views
Puzzling behavior produced by Exists
I need to simplify a set of solutions of a system, say for example:
...
