Questions tagged [equation-solving]

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

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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: ...

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