Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
6,379
questions
2
votes
1
answer
214
views
Parametric Plotting 6D Dimensions to 3D for Visualizing a Solution
I am trying to find out when: $$f(x,y,z,α,β,γ):= z\cos(β)\cos(γ)+y(\cos(γ)\sin(α)\sin(β)+\cos(α)\sin(γ))+x(−\cos(α)\cos(γ)\sin(β)+\sin(α)\sin(γ)),$$ where $α,β, \text{and } γ$ can be any value in $[-2\...
- 403
2
votes
0
answers
75
views
Solve state space equations
I never used Mathematica before. But I need to solve this system of equations for xt0, xt1, xt2, t1, t2. Everything else is given.
xt1,xt0, xt2 are 5x1 matrices. t1 and t2 are numbers. The code below ...
- 21
0
votes
0
answers
36
views
Commutator for Solving Coefficients in a Hamiltonian
I am relatively new to Mathematica but I understand the basics.
I want to solve for coefficients by commutator constraints and I have problems implementing the commutator. The setup is the following:
...
- 1
0
votes
0
answers
44
views
Identify a condition among variables that satisfy an inequality
I have a symbolic function that produces the output
a = (1 - e - mu/n) Log[(1 - e - mu/n)/(1 - mu/n)] + (e + mu/n) Log[((e + mu/n) n)/mu]
If I substitute ...
- 424
0
votes
0
answers
35
views
Indefinite time for Reduce a set of conditions
Following command is taking too ling time to run.
...
2
votes
1
answer
194
views
How to replace==in the equation with ->?
It is required to replace the ==
in equation
2b==E ^ x0- x0
with ->,
becoming:
...
- 2,905
1
vote
0
answers
55
views
Unsolvable system of equations - NSolve takes too long to run
I am trying to solve a system of 6 equations. Here is my input values:
...
- 341
3
votes
1
answer
132
views
Solve Differential Equation Numerically
I investigated my system and encountered differential equation such as
$y''(x) = e^{y(x)}-e^{-2y(x)}-e^{y(x)-y(x+d)}$,
where $d$ is a constant. The boundary condition is
$y'(0) = 30$
$y'(\infty)=0$.
I ...
- 33
0
votes
0
answers
51
views
How to create a relational expression(=equation) from a complex parameter?
I obtained the following parameters in the process of solving a problem.
...
- 1,522
1
vote
1
answer
67
views
Simpson's rule code
I could swear I'm doing this correctly but the answer is just off every time for Simpson's rule. Any help?
...
- 11
1
vote
1
answer
88
views
A code for producing system of equations for central difference method
I am trying to solve the differential equation $y''(x) = y(x)+\sin[y'(x)]$ numerically over the interval $[0,1].$ Now using central difference method I arrived at the equations of the type
$$ y_k = \...
- 219
0
votes
1
answer
82
views
Solving differential equation with hyperbolic functions
I've been trying to solve the following differential equation:
\begin{equation}\left( \frac{d \tau}{d \sigma} \right)^2 = \frac{(E_0 \cosh\sigma-p_\tau\sinh\sigma)^2}{(E_0 \cosh\sigma-p_\tau\sinh\...
- 47
1
vote
3
answers
244
views
Root finding for holomorphic functions
Mathematica's FindRoot has a lot of options, but the documentation is not helpful for what I would have expected is an important case, numerically finding complex ...
- 1,111
0
votes
0
answers
53
views
Rounding the solution of NSolve
How do I round x and y solved in the equation to only integer solutions?
I get an error no matter where I put ...
- 406
2
votes
2
answers
152
views
Newton Raphson with continuation error
I have here an algorithm to solve multivariable nonlinear systems using the Newton-Raphson method with continuation. However, there is some error in the code that I am unable to identify, causing it ...
1
vote
2
answers
89
views
Solve a non-trivial matrix equation for an unknown matrix
I am solving the matrix equation to pass from the Fokker-Planck to the Langevin equation. Specifically:
\begin{equation} D=BB^T
\end{equation}
where
$$ D=
\left(\begin{matrix} l x_1(1-r_1) + e_1 r_1 ...
2
votes
1
answer
119
views
Visualizing the zeros of a function of three variables
I have a function f[x_, y_, z_] := (x - y) (z^2 - x*y) of three variables x, y and ...
- 471
4
votes
1
answer
70
views
Commutant of set of matrices
I'm trying to compute the commutant of a set of matrices, so the set of matrices that commutes with all matrices in the original set.
I'm a complete newbie with mathematica, so I would be greatful for ...
- 43
1
vote
1
answer
153
views
0
votes
2
answers
83
views
Set of differential equations with trigonometric functions and a derivative squared
I've been trying to solve a set of differential equations that involve the square of a derivative, similar to another post I made here, and trigonometric functions, as seen here
\begin{equation} \frac{...
- 47
5
votes
1
answer
72
views
Modeling Infection Spread among Different Age Groups with Contact Matrix
In this code, we divided the population into children, adults, and old people.
The probability of infection per contact, $b$, is 5 % for people of all ages
The total population size is 1 million, and ...
2
votes
6
answers
468
views
All solutions that satisfy $ x_{1}^{5}+x_{2}^{5}+x_{3}^{5}+x_{4}^{5}-x_{5}^{5}=0 $
I want to find a combination that satisfies all the solutions of the following formula.
$$
x_{1}^{5}+x_{2}^{5}+x_{3}^{5}+x_{4}^{5}-x_{5}^{5}=0
$$
$x_{1}$, $x_{2}$, $x_{3}$, $x_{4}$, and $x_{5}$ are ...
- 736
7
votes
2
answers
638
views
The Poincaré Sections of Yang-Mills-Higgs System [closed]
In the papers Quantum Chaos in a Yang-Mills-Higgs System and DIFFERENT FACETS OF CHAOS IN QUANTUM MECHANICS, the authors have plotted three Poincaré sections for different values of ...
- 1,554
0
votes
1
answer
105
views
How to implement the Vieta's formula in Mathematica in the general case? [closed]
I have list of $N$ roots ($r_1, r_2, ..., r_N$) and would like to restore some coefficient $a_k$ of the original polynomial. Vieta's formula is what I need, but I don't understand how to implement it ...
4
votes
2
answers
446
views
Solving coupled differential equations involving the square of the derivative
I want to solve the following system of coupled differential equations in order to obtain particle trajectories:
\begin{equation} \frac{dt}{ds} = (E-y\, p_t)y \end{equation}
\begin{equation} \...
- 47
3
votes
1
answer
86
views
Discriminant of the equation have three integer solutions m
I have equation
(x+9)(x^2+(m+1) x-7 m+8)=0.
and
Solve[Discriminant[(x + 9) (x^2 + (m + 1) x - 7 m + 8), x] == 0, m]
{{m -> -...
- 2,595
2
votes
3
answers
132
views
How to find the number of real roots for this equation?
I want to find the number of real roots that satisfy this equation:
f[g[x]] - h[f[x]] == (a)^2
Where:
...
0
votes
1
answer
33
views
Where did the matching transfer go wrong?
For the equation:
4 m^2 + 6 n == 1 + n^2
shifting the term yields this:
4 m^2 == 1 + n^2 - 6 n
I tried this, but how did it ...
- 2,905
1
vote
3
answers
267
views
Solving Geodesics from Christoffel Symbols
I am somewhat new to using Mathematica and I am facing difficulties with a specific problem related to the geodesics of Einstein's field equation in a vacuum.
The metric I am working with is derived ...
- 11
0
votes
0
answers
52
views
Using a module that turns the output of Findroot into a function of a variable
I am trying to create a module that finds the root b* of some equation with two variables b and ...
0
votes
1
answer
63
views
A specific usage of "Solve" function [duplicate]
It is something from Simplifying polynomials with conditions on variables, that intend to minimize the number of variables.
The problem is the usage of ``Solve". I know how to solve equations, ...
- 115
1
vote
0
answers
78
views
Solving Diophantine Equation with Only Specific Variable Values Allowed
I am trying to Solve an equation like this:
$$
\sum _{i=1}^{\text{iMax}} (-i+\text{iMax}+1) n(i)=546
$$
Where all the $n(i)$ are can only take on the values 2,3,6,7, or 8.
I really have no idea how to ...
- 3,548
0
votes
0
answers
66
views
NSolve can't solve a system of 2 equations with 2 unknowns
I've been trying to solve a system of 2 equations with 2 unknowns using NSolve. But It's been too slow. I waited for more then an hour without any results.
The code is:
...
- 101
0
votes
0
answers
50
views
Symbolic computation using ``Reduce" does not give a result
Firstly, I have proved that γ = β^2/12 is one of the solutions of (A12 P312 + A13 P213 + A23 P123)/P123123 + A12 A13 A23==0
<...
- 115
4
votes
3
answers
255
views
How to solve the equation to obtain the specified form?
Solve the equation to obtain such a result form;
...
- 2,905
0
votes
1
answer
70
views
Finding coprime solutions to Diophantine equations
I'm hoping to use Mathematica to find solutions to Diophantine equations. Below is a toy example of something I would like to try.
Consider the case of $$x^2+y^2 = 17$$
which has the solution $x=1,y=4$...
- 225
3
votes
1
answer
175
views
Extremum of the graph of a function has integer coordinates
Graph of the fuction $y=\dfrac{(x-26)(x+9)}{(x+14)(x+19)}$ has maximum point and minimum point are (-16,-49) and (-4,-1) whose ...
- 1,000
1
vote
2
answers
96
views
Solving a-two-variable equation in primes
How solve the following equation in Mathematica (preferably in one line) for pairs of $(x,y)$ such that $x$ and $y$ are primes?
$x^3-y^4=1$
- 115
2
votes
2
answers
100
views
How to eliminate special cases from a solution?
When I solve a system of equations with Reduce, it will give me as possibilities that system parameters can be exactly some special value that will allow the ...
- 761
1
vote
0
answers
48
views
Stiffness problem which abruptly stops the evaluation
We have a Lagrangian and we found the EOM. We need to solve the EOM and find the Phase-space plot. However, we are facing a stiffness problem which abruptly stops the evaluation (...
- 1,554
-1
votes
1
answer
80
views
How to get the range of analytical solution of inequalities?
Is there a way to get the range of analytical solution of inequalities? Such as:
...
- 465
2
votes
1
answer
48
views
How to explore the unchanged eigenvalue with the largest real part?
The provided code below employs the Chebyshev collocation method to calculate eigenvalues. I'm interested in examining the eigenvalue with the largest real part while ensuring it remains almost same ...
- 47
0
votes
1
answer
52
views
0
votes
1
answer
117
views
2
votes
2
answers
214
views
Performing maximum likelihood estimation for SIR Model
The code first produces a plot of the dataset, then simulates the SIR model using the parameter values we found in the manual calibration to the full dataset of the total number infected .
...
1
vote
1
answer
82
views
Proving an expression from Mathematica which is clearly visible from Plots
I have the following Mathematica code:
...
- 899
0
votes
1
answer
64
views
Writing a sum-of-squares function or SIR model fits
I am trying to write a function that calculates and returns the (sum-of-squares) value (SSQ) for the fit of a simple SIR model, parameterized with given values of $\beta$ and $\gamma$, to any dataset.
...
1
vote
2
answers
198
views
Solving an equation that contains u and (1-u) as variables [closed]
How can the following equation be solved using Mathematica, as the equation contains u and 1-u?
...
- 51
1
vote
0
answers
75
views
Problem with the Manipulate command
I am trying to upload a notebook with the following code to my blog, but every time I upload it, the "manipulate" code does not give anything. Do I have to change anything?
...
0
votes
1
answer
61
views
Solving the system of equation with the expression of total differentiation using Cramer's rule
I want to solve the following system of equations of total differentiation using Cramer's rule.
And I got the following message:
where d is delta as the symbol of ...
- 113