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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27 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 ...
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1answer
52 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 ...
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1answer
117 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 ...
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1answer
40 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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1answer
49 views

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” ...
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46 views

How to solve a system of equations with an incomplete elliptic integral?

I have a system of five differential equations of second order with ten boundary conditions. Each differential equation corresponds to a given interval. I solve, by hand, and found nine clear ...
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0answers
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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 ...
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1answer
55 views

How to Solve for X? [on hold]

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 ...
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50 views

Gaussian eliminaton [on hold]

Algorithm in Mathematica to solve this system with Gaussian eliminaton E1 : x1-x2+2x3-x4 =-8 E2 : 2x1 - 2x2 + 3x3 - 3x4 = -20 E3: x1 + x2 + x3 = -2 E4 : x1 - x2 + 4x3 + 3x4 = 4 My attemps were ...
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1answer
27 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 ...
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1answer
35 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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1answer
73 views

(Row?) reduction of a system of equations

For a mathematical problem I am trying to solve, I have (say) $(N+1)$ inhomogeneous linear equations in $M$ variables of the form $$\sum_{a=1}^{M}c_{i a}p_{a} = \xi_{i} \quad \text{ where } i=1,\...
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42 views

NIntegrate: integrand can not evaluated numerically [on hold]

I am trying to solve an integral equation given below, how do I overcome the sampling points error as shown in the figure below Here is the code: ...
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1answer
92 views

Shooting Method for Numerical Solution

I am trying to solve the following nonlinear differential equation using the shooting method. The equation is a boundary value problem with boundary condition x[0]=Pi and x[Infinity]=0. In order to ...
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1answer
66 views

how to solve equations

I am trying to find the values of L and \theta, but mathematica is unable to produce output. My code is given below, where the value of k is fixed, i.e., 0.75, but the value of B can be positive or ...
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3answers
379 views

How to set a tolerance level for equality constraints

Given two equality constraints: x+y==250 and z+p==65 where x=190, y=50, z=45, p=15, I want ...
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1answer
255 views

Unable to find solution to 6 simultaneous equations

I have 6 equations: $$\begin{array}{l} x_1^2+y_1^2=(x_2-x_1)^2+(y_2-y_1)^2 \\ x_3^2+(3-y_3)^2=(x_3-x_1)^2+(y_3-y_1)^2 \\ 4[(x_3-x_2)^2+(y_3-y_2)^2]=(4-x_2)^2+y_2^2 \\ x_2^2+y_2^2=4(x_1^2+y_1^2)\\ 4[...
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2answers
50 views

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}, ...
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0answers
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 ...
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1answer
28 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 ...
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2answers
61 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 $\Phi<0$ ...
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2answers
128 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 ...
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2answers
37 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 ...
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3answers
219 views

Problems with solving PDEs

I am using NDSolve to solve the two equations: ...
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1answer
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 ...
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1answer
31 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 ...
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1answer
52 views
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1answer
66 views

how to solve this system of equations with a parameter

I am a selflearner and really new to mathematica software and I am struggling to solve the following system of equations...: $(x-d)(y-d)+3(x+1)(1-y)=0$ $(x-d)^2+3(x+1)^2=(y-d)^2+3(1-y)^2$ $(z-x)(y-...
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0answers
40 views

Edited Ques: FindRoot returns the initial guess (Having large magnitude) [closed]

In my program (Main Program, data File), I am trying to find the root of equation by FindRoot in range of order of $10^{12}$ for the variable ss at the end of ...
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0answers
74 views

Why does FindInstance find a wrong instance to this problem?

When I ask for an instance in a six-variable problem, Mathematica [version 9] returns an instance that is wrong. (Both of the first two equations are False under ...
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0answers
32 views

Output of Reduce + Simplify

I'm using Reduce to solve some equations and then simplify to eliminate some undesired results. The problem is that, when I apply Simplify, it messes with my output from reduce. As an example: ...
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2answers
80 views

Problem with FindRoot function

I have set up a code to solve simultaneous integral equations. These result essentially from taking integrals of the Fermi-Dirac distribution. Although there are no obvious problems with the code it ...
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1answer
47 views

Remove +0Is from Root function

I'm trying to find the zeros of the eigenvalues (functions of $k_x$) of a self-adjoint $4\times4$ matrix H: ...
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0answers
16 views

Expressing Numbers with Rational Denominators (Surd Form) [duplicate]

Is there a command which expresses given real numbers in surd form (when possible)? That is, a form where any rooted terms are placed in the numerator, and the denominator is rational. Here are some ...
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0answers
101 views

How do I Solve for the value of a function? [closed]

I have a function used to calculate the Optical Depth of the CMB. You can find the full notebook source here Optical Depth Repro.nb ...
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0answers
32 views

Simplifying a square root of expression containing non-polynomial term

I have the following expression: $\qquad \sqrt{(\delta-k)s^2+(k-\lambda)s+\beta s^{\epsilon}(s-1)+\alpha}$ where $k$, $\delta$,$\alpha$,$\lambda$ and $\beta$ are constants and ($0\leq \epsilon\leq1)$...
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1answer
68 views

Help me with understanding root objects [duplicate]

I solved an polynomial equation of degree 20 and got root objects as solutions. I cannot understand how to match such output to any standard analytic form. After studying ...
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0answers
31 views

How to compute a system of ordinary differential equations with initial condictions over a continuous range

I have some questions about Mathematica programming and would appreciate if you could help me. I want to solve a system of ordinary differential equations \ [Mu] '[t] and \ [Lambda]' [t] and each ...
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0answers
74 views

NSolve not solving my transcendental equation

Would be grateful for your help in tackling this complex polynomial where I am trying to solve for x. When I run the code below, I get the message: value x of ...
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1answer
75 views

Numerically solve system of 64 equations with 64 variables in matrix form

I have 2 matrix $A$ and $B$ both of size 16x16. Most of the values $A_{i,j}$ and $B_{i,j}$ for the same couple $(i,j)$ are equal to 0. The remaining ones are a positive floating number for $A$ and a ...
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0answers
50 views

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 ...
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0answers
37 views

What is used for the % symbol in mathematica? [duplicate]

Im new in mathematica i want to know logic about this program. I got this code: {{vo, vn, Ii}} = {vo, vn, Ii} /. %; i know that the syntax /. is for replacement but i dont know whats going on with ...
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1answer
53 views

Can't solve system of six equations in five variables

Here's an equations from mechanics: ...
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0answers
30 views

How to solve this set of linear equations

I am trying to solve six linear equations, for which a solution exists (since it can be recovered by Matlab). I am trying to reproduce it here. I have the following MWE: ...
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3answers
69 views

expression containing radicals of imaginary numbers

I can't bear an expression containing radicals of imaginary numbers, in case it can be expressed as in terms of radicals of real numbers only. For example, I can't bear the expression Sqrt[2 + i] ...
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1answer
25 views

Equation solving for approximate solutions when function has numerical integration in it

I have an equation that is of one variable lat and has a numerical integration in it t from 0 to 1. Let's say it's given by <...
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41 views

Error message from FindRoot

I am getting the following message when I evaluate a call to FindRoot: The line search decreased the step size to within tolerance specified by AccuracyGoal and ...
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1answer
154 views

Solving multi-field problems in MMA 11.3

Based on the PDE model proposed by @Schumacher Solving a second order coupled PDE system, the one dimensional multi-field Problem I would like to solve such benchmark test: namely: u(x): ...