Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
6,505
questions
15
votes
6
answers
2k
views
How to solve this matrix equation
How to solve the following matrix equation?
Solve[MatrixRank[{{1, x, 3},
{2, 4, 5},
{2, 4, x}}] == 2, x, Reals]
8
votes
2
answers
399
views
Asymptotic inverse function?
A paper I am reading defines a variable $\theta$ in terms of another variable $\phi$ as an expansion in $u$, where $u$ is understood to be small:
$$\theta=\phi-u^2\sin\phi+\mathcal{O}(u^4).$$
They ...
1
vote
2
answers
83
views
Reduce and FullSimplify don't reduce fully -- how to check if candidate solutions hold
I have a big system of equations and want to check if some candidate solutions hold.
Ideally, I want to have an expression that returns 'True' if my candidate solution hold and 'False' otherwise.
...
0
votes
0
answers
29
views
Solve gives odd answers [duplicate]
I am running this, and it should give me a number t with preferably many decimals, but the output is odd:
Solve[8/(t + 2)^2 + 2/(t + 1)^2 == 1, t, Reals]
Thank you
0
votes
1
answer
118
views
The Range of a Function
I would like to see minimum and maximum for this example!
g[x_]:=(3 a - 2)/((2 + 3 b - 3 a) x^2) + f*x^(-3 a + 3 b + 2)
also for those parameters "1 < a &...
5
votes
1
answer
130
views
Strange issue with NSolve
Please can someone explain to me why the first of the following fails to run (just spitting back the input without warnings/errors), while the second executes successfully?
...
1
vote
1
answer
121
views
Problem in getting coefficients list of power series solution of y''[x]*y'[InverseFunction[y][x]] - y'[x] == 0?
I have tried to get solution of the following ODE:
y''[x]*y'[InverseFunction[y][x]] - y'[x] == 0
Using the code given below, the solution is a formal power series ...
2
votes
2
answers
556
views
How to code a sum in Mathematica and how to solve it?
I'm trying to find the coefficients of the Radau IIA Runge Kutta Implicit scheme.
Those Runge Kutta schemes have Butcher tableau consisting of Cs, As, and Bs.
article
I have already computed the Cs as ...
2
votes
2
answers
244
views
NSolve gives weird result for $n=101$ with NSolve[$\frac{d}{dx}\prod \limits_{k=1}^n (x-k)$==0,x]
Coming from this post: What would be the roots of the derivate of this polynom I did a quick check with Mathematica and arrived at a wrong result. I was initially confused but chose to trust ...
6
votes
2
answers
113
views
Reduce an expression where the variables can assume only $\pm 1$
I would like to solve this equation:
x1y1 + x2y2 + x3y3 + x4y4 = 0
and I would like to count the number of distict solutions.
Here $x_1,\dots,x_4$ and $y_1,\dots,...
3
votes
1
answer
58
views
How to detect the positive solution to this logistic boundary value problem
I am trying to find the positive solution to this nonlinear ODE. Theoretically, it has been proven that this problem has a unique positive solution for lam large. But, Mathematica can detect only the ...
0
votes
1
answer
173
views
How to find the value which minimises the residual sum of squares
I have 3 equations with 3 parameters(unknowns). I would to solve it using newton raphson method. I want to use initial values (parameters) for the Newton Raphson
procedure as the value (parameters) ...
3
votes
2
answers
400
views
Solving hyperbolic equation with parallelization in python by elucidating Mathematica algorithm [closed]
So! I have what seems like a rather basic hyperbolic equation to be solved written in Mathematica, with an integer input ‘n’, for which I am seeking the First {x,y} Integer solution to satisfy the ...
0
votes
0
answers
51
views
Use Solve solutions as Function when there are multiple solutions on distinct domains
First, I'm sorry if this question is a duplicate. I am very new to wolfram, and I have tried many solutions found here without success.
For the context, I have at hand a method to produce successive ...
0
votes
4
answers
115
views
Solve conditional term with mathematica [duplicate]
Solve mathematical conditional expressions with Mathematica, e.g if $x+y=3$ and $xy=-1$ , what is result $\frac{x^3+y^3}{x^2+y^2}$
2
votes
1
answer
199
views
The root of the trinomial equation z^n+2*z-t written in terms of FoxH
From documentation, the roots of the general trinomial: $$z^n-z-t=0$$ are written in terms of FoxH special function;
...
8
votes
2
answers
832
views
Numerical solution to a nonlinear Ordinary Differential Equation
I am trying to solve the following ODE for $f(x)$:
$$x f' - f = \frac{(f')^2}{\gamma^2}[1-({f}')^\gamma]^2$$
where $\gamma < 0$ and real, which makes the ODE highly nonlinear. Since I am not ...
0
votes
1
answer
100
views
Solving a particular transcendental equation
I am trying to find the chemical potential as a function of number density, the equation of which is
\begin{equation}
\frac{n}{2\pi l_{B}^2} = \int_{-\Delta}^{\Delta}d\epsilon \frac{e^{-\epsilon^2/w^2}...
1
vote
1
answer
119
views
Find the all cases that satisfy an equality
I want to find which cases the following equality is satisfied.
...
2
votes
1
answer
87
views
Inequality cannot be solved using Reduce (no transcendental functions) [closed]
I have these assumptions:
...
6
votes
1
answer
719
views
Maxwell construction problem with FindRoot
A Maxwell construction is just an integral of area and then solving for a root to find vapor pressure.
This must be exactly the same value as where the Gibbs energy plot crosses at a point. I found ...
13
votes
3
answers
959
views
Routh-Hurwitz criterion not giving correct answer when done manually?
Consider the system:
\begin{align}
\frac{dS}{dt} &= \nu N -\frac{\beta S I}{N} + \xi R - \nu S\\
\frac{dE}{dt} &= \frac{\beta S I}{N}- \sigma E -\nu E \\[2ex]
...
2
votes
2
answers
147
views
Rewriting an expression while using another parameter
I wish to rewrite V and M with the given A. I have provided what the end result is supposed to look like.
Here is V
...
1
vote
0
answers
27
views
Syntax of wolfram alpha solution entry (using #1 and &) [duplicate]
I try to understand the solution that solves the following equation
https://www.wolframalpha.com/input?i=argmin+%28f%28x%29%3D%28x%2F%28a-x%29%29%5E2*b%2Ba-x%29+for+a%3E%3Dx%3E%3D0
It is written that ...
1
vote
1
answer
113
views
Why Reduce command dosn't work in my below code? [closed]
I have tried to solve the following equation as shown in the code using Reduce command, but I can't solve for the values of a, <...
3
votes
3
answers
132
views
Converting solutions back to equations (inverse of ToRules)
If I solve an equation (or a system of equations), I get output like
{{a -> 5, b -> 4}, {a -> 2, b -> 3}}
I would like to convert this a statment, like
...
2
votes
0
answers
98
views
Defining new Domain for variables
I am trying to define a new Domain for variables to use with functions like FindInstance or Solve. For example, If I wanted to solve x+y+z=1 over the Reals, I'd get a large solution space. But If I ...
0
votes
1
answer
59
views
Get Real Solutions works in Solve but PositiveReals don't (Quantities)
I'm trying to get the R+ Solutions to a school problem with solve. Everything works fine with Dom -> Reals but when I try ...
0
votes
1
answer
85
views
proving closure for vector space
I would like to present to my students, closure under vector addition (same situation for scalar multiplication).
I have found that this works fine:
...
1
vote
1
answer
64
views
Symbolic Solution to Rational Equation [closed]
I have the following equation, which I would like to solve for a in terms of x, y, and ...
0
votes
2
answers
279
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;
...
1
vote
1
answer
97
views
NSolve for Piecewise function
I have a piecewise function. I want to find the root of this function with the NSolve command. But, it does not give me any result and it just prints the equation. I can find the root with FindRoot, ...
0
votes
1
answer
376
views
How to obtain non-zero solution of the given system of equations?
I have this system of six equations for $\{x,y,z,u,w,v\}$.
...
5
votes
2
answers
481
views
Is there a Mathematica equivalent of Eq() in sympy
In sympy, the Eq() function could help to visualize a system of equation like below, I am wondering is there an equivalent of Eq() in Mathematica? Thanks!
4
votes
2
answers
1k
views
Inverse function of y = x + (0.022 - x) ^ 1.414?
I'm a software engineer with math classes through differential equations about 15 years in my past, and I've gotten stuck trying to invert an equation.
The equation:
$y = x + (0.022 - x)^{1.414}$.
In ...
0
votes
1
answer
78
views
How to plot an implicit function with real and complex solutions, different line styles/colours, and a double y-axis?
I am new to Mathematica and trying to reproduce the following figure using ContourPlot:
(From: https://iopscience.iop.org/article/10.1088/1402-4896/abb2e0/meta)
My ...
0
votes
2
answers
96
views
How to print the function of $f[n]==f[n]$?
The funciton is as follow,and n can be 1,2,3...
f[n_] := n + n^2 + n*a + (2*n + 1)*b;
f[1]
f[2]
...
0
votes
0
answers
52
views
RSolve[] gives error RSolve::litarg when solving demo equations from the official documentation
The official documentation of RSolve[] (specifically, in the fifth paragraph of the seciton "Details and Options") states that:
The specification a∈Vectors[m] or a∈Matrices[{m,p}] can be ...
0
votes
2
answers
175
views
Reduce an inequality
I have this inequality I don't know why it is not working?!
...
0
votes
2
answers
406
views
Power::infy: Infinite expression 1/0. encountered
I am trying to solve the following linear system consisting of four unknowns.
...
0
votes
2
answers
139
views
NONLINEAR EQUATIONS cannot get the solution
I have simplified the equations and decrease the variables to 5, and changed the parameters' value as I think the equations in enter link description here is because of the improper parameters' value.
...
1
vote
2
answers
220
views
FindRoot::jsing: Encountered a singular Jacobian at the point when solving NONLINEAR EQUATIONS
I have tried many methods to solve the following nonlinear equations.
...
5
votes
1
answer
442
views
How to solve for composition function?
If $ f(x)=x+6, h(x) = 6x-2$ and $g\circ f = h$, how can I solve for $g(x)$? I know how to do it on paper, but I wonder if Mathematica can do it in a general way. This doesn't work:
...
0
votes
0
answers
84
views
Bug in RootSearch
I ran into a problem with Ted Ersek's RootSearch (https://library.wolfram.com/infocenter/Demos/4482/) while solving the problem described here. ...
1
vote
1
answer
49
views
Change domain of kinetic functions in order to fit with ParametricNDSolve
I'm trying to solve kinetic differential equation depended on time with three parameters: preexponential factor a, reaction order ...
0
votes
1
answer
144
views
Mathematica gives different zeros of polynomials
I have defined the Jacobi polynomials in terms of hypergeometric functions in two ways. While calculating the zeros of Jacobi polynomials, Mathematica shows different values of first few zeros. I am ...
1
vote
0
answers
55
views
How to run RootSearch with increased WorkingPrecision?
I have a Sturm-Liouville problem on a finite interval $0\leq z \leq 1$. I integrate the one-dimensional ordinary differential equation of the second order (the LoDestro equation) by the shooting ...
0
votes
1
answer
148
views
How to avoid Mathematica output the simplified the squared root term by factoring some coefficient
When I use Mathematica to calculate some roots of an quadratic equation, it will output the simplified answer like $\frac{-w \sqrt{-h} \sqrt{4 \theta ^2 p-4 \theta p-h}+h w+2 \theta p w}{2 \theta ( ...
1
vote
0
answers
36
views
answers Solving puzzles with Mathematica [closed]
Hi, I want to calculate the values of these numbers a, b and c.
The only information I have:
a = √((b-c)²)
b = a * c
c = (a+b)/2
Anyone knows where to begin?
6
votes
3
answers
454
views
Linear ODEs with NDSolve
I am trying to solve some first order linear odes. My code is below:
...