# 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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### 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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### 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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### 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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### 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” ...
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### 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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### 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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### 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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### 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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### 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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### 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}, ...
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### 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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### 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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### 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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### 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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### 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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### Problems with solving PDEs

I am using NDSolve to solve the two equations: ...
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### 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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### 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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### 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 ...
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### 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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### Can't solve system of six equations in five variables

Here's an equations from mechanics: ...
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### 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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### 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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### 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 <...