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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Hybrid ODE simulation with very small parameters

I am trying to solve a Hybrid dynamical system using NDSolve and WhenEvent. I am able to simulate when the parameters are close ...
46 views

Numerically solve equation

I have an equation, that I want to solve numerically. The equation is $$x(1-cx)-\frac{xy}{1+x^{1+\gamma}}=0$$ The problem here is the $\gamma$. What I want to achieve is a plot of the solutions in ...
59 views

Reduce taking long time on six equations

I have a system of equations, 4 linear and 2 quadratic, of the following form: $$L_{i,j}(x_1, \cdots, x_{12}) = \sum_{k=1}^{12} x_k c_{k,i,j}$$ for $i, j = 1, 2$, i.e. the $L_{i,j}$ are the ...
30 views

Is there any way to terminate the evaluation of NSolve whenever it finds a solution?

NSolve numerically finds all the solutions, which satisfy all the constraints, of an equation. My question is: Is there any way to automatically terminate the evaluation once it finds the first ...
25 views

Trying to solve equation with changing variables. However only care for the real positive answer number

Warning: very new to Mathematica Currently I am trying to solve for x, but the variable K changes. So I'd like a value for <...
191 views

Include boundary conditions in wave equation solver

I'm solving a wave equation using mathematica. I already included the initial displacement and velocity. However, I don't seem to be able to include boundary conditions $u(-\pi,t)=u(\pi,t)=0$. ...
32 views

Making a List of FindRoot approximations

I have the following function. c[n_, k_, z_] := Sum[(-1)^j*(z^(n*j + k)/(n*j + k)!), {j, 0, Infinity}] I'd like to find roots of the equation ...
77 views

About some hypergeometrical formulas for roots of trinomial and quadrinomial

Please correct my interpretation of formulas by Pietro Majer from post. For equation $a=x+x^p$ one root is $x=a\sum\limits_{k=0}^{\infty}\frac{(-a)^{(p-1)k}}{(p-1)k+1} {{pk}\choose{k}}$ Wolfram ...
39 views

Mathematica is not solving a nonlinear equations system with variables powered to rational exponents

I am trying to solve a system of 3 equations with 3 variables in Mathematica. The issue is that in this equations I have several parameters, and this makes the involved variables to be powered at ...
57 views

recurrence equation

The output of Mathematica is only a copy of the input. What am I doing wrong? ...
72 views

FindRoot - Convergence Failure

In my problem which I try to solve with FindRoot in Mathematica version 12 I usually get the following errors ...
69 views

Facing error while solving a determinants with the use of NSolve inside module

I have written a small program to find the natural frequencies of some system using an energy approach. v1 and t1 are the potentials and kinetic energy of the beam. v2 and t2 are the potentials and ...
82 views

How to solve set of linear differential equation in Mathematica?

I have a set of linear differential equations and are written in this format [X']=[Y]-[R] where [P][Y]=[Q] My actual P matrix size is of 20x20 and Q is of 20x1 and Y is of 20x1. I have written this ...
125 views

Wrong result by FindRoot

Slight background: I am trying to find the coexistence reduced pressure ($p_r$) of a Van der Waals fluid at a reduced temperature of 0.85, this requires finding the solution to the following system of ...
53 views

Asymptotic solution of a second-order ODE containing InverseFunction

Essentially, I have a second-order differential equation given by ode below. In order to solve it, I need to obtain an asymptotic solution where $g(x)$ must vanish at infinity which will be used after ...
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Is it a mistake in the formula or inaccuracy in the calculations of numerical integration?

Formula for roots of trinomial $\displaystyle z^m-az^n-1$ with definite integration from paper Лахтинъ, “Выраженiе корней трехчленнаго алгебраическаго уравненiя посредствомъ опредѣленныхъ интеграловъ” ...
77 views

Does such prime $P$ exist? [migrated]

The equation $(10^{6n+1}-54n-10)($mod P$) = 0$ , find the value of prime P such that there are AT LEAST 3 solutions for n > 0 , whose values of n are all below (P-1)/6. I don't even know how to solve ...
58 views

How to Solve for X? [closed]

Have Mathematica solve sin(x) = 0 for x. What I did was h[x] := Sin[x]; and Solve[h[x] == 0, x, Reals] // N but its giving me a really weird answer . What would be the proper way of ...
30 views

NSolve with Interpolation function

I am trying to apply NSolve to an Interpolation function which I have evaluated before. For a function of 1 argument everything works out but as soon as I try to apply the procedure for a function of ...
41 views

How can I get output in decimal instead of fraction?

I am trying to solve a simple equation but I cannot get the answer with decimal, how can I do it? I want FS1 and FN1 with decimal. ...
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Why does this FindRoot code only trace one of two roots?

I have written the following code to trace the roots (in terms of f) of the shown equation as n rises. There are two roots for a given value of n. For example for n = 2, the roots are {f -> 0.171573}, ...
34 views

Trying to extract the first four roots of an transcendental equation, but could not able to decide which are the first four roots

I am trying to find the roots of the transcendental equation, for that, I have used NSolve function, but when I search for roots of b between 0 to 20, it will produce empty list, If I change the ...
29 views

Solving a polynomial equation involving gamma function

I am trying to solve an equation having degenerate limit of Fermi-Dirac integral. My code basically is ...
62 views

NSolve an equation and its first derivative

Consider the following plot: Plot[(22500 + T^2/3) ϕ^2 + 320 ϕ^3 + ϕ^4 /. T -> 96.43650760992945`, {ϕ, -200, 20}] I would like to find the value of $\Phi<0$ ...
129 views

I am quite positive that this function is non-negative — How to calculate/proof

I have this function and running some experiments with the 3DPlot shows that this function "must be" non-negative (formerly I wrongfully asked for positivity) everywhere. However, the Reduce does not ...
52 views

Trying to to replace Root expressions from the output of Eigenvalues by the explicit forms

When I calculate the eigenvalues of the following matrix (H) by using Eigenvalues, I get complex expressions with ...
224 views

Problems with solving PDEs

I am using NDSolve to solve the two equations: ...
71 views

DSolve returns unevaluated(I need a closed or numerical solution for this system and plot solution)

I am trying to find a solution to this system of differential equations but the program gives the same output without any messages. I would like help. Please find the Mathematica code posted here. a ...
33 views

Selecting solutions that evaluate to positive

How to extract symbolic outputs of Solve that evaluate to positive at given values of parameters? For example, if ...
52 views

Reduce, Piecewise function gives result that does not make any sense given condition constraint

Here is my code: ...
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How to apply the utility Packages for Numerical Differential Equation Solving

I have solved two coupled equations with {Solf, Solg} = NDSolveValue[eqns, {f, g}, {x, 0, L}, {t, 0, tmax}] and want to extract the computational grid ...