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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87 views

How solve this nonlinear equations system by 12 unknowns?

We consider the following integral equation of mixed type: $x[t]=\frac{t^4}{6} -\frac{t^3}{3} +t+\Sigma_{\mu=1}^2\int_{0}^t k_\mu[t,s]G_\mu[s,x[s]]ds ,0\leq t\leq 1 $ ; (1) where $k_1 [t, s] = s^3$...
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0answers
54 views

Find correct boundary value to solve an ODE

This is the first time I am seeking help on this site. I am not sure whether the problem can be sovled. Actually, I am trying to solve an ODE ...
3
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2answers
117 views

How to find a solution in terms of vars which satisfies equation for any value of x?

I am porting some Maple code I wrote to Mathematica. In one place, I use Maple's solve with what Maple call, identity. The help page for this command is here What is Mathematica's equivalent of ...
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3answers
80 views

Given f[b,d,k]=0 and g[b,d,k]=0, I need to find a branch (provided it exists) of k[b,d] such that this system has a solution in b,d

I have two polynomials in k given by f[b,d,k] and g[b,d,k]. I know that there exists a ...
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1answer
69 views

Solution for inequality equation - “Cannot be solved with the methods available to Reduce”

I am trying to solve the following inequality for $v$: $b>e^{\frac{-v}{\alpha}}\cdot \alpha + v$. (Where I know: $b>0$, $v \in [0, 1]$, and $\alpha >0$). However the following doesn't work: <...
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1answer
47 views

Using FindRoot on a function defined with FindRoot

Simplified starting point: I have a function of two variables f[a_, x_] := x^2 + a^2 - 4; and define a function that gives an x ...
5
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2answers
156 views

Plotting of probability density on a lattice and studying dynamics

I have a lattice described by a AdjacencyMatrix or Hamiltonian. This matrix has all the information of how each site is connected to another site with what hopping ...
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2answers
73 views

Why does this simple code with Eliminate not give any result?

My goal is to obtain the function $s$ defined in the code below as a function of $\chi_1$, $\chi_2$, $\chi_3$. The code runs but never ends, although the problem does not seem too hard to solve for a ...
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2answers
79 views

Equation solving to find a matrix

If I have the vector z={y1+2*y2+y3,y1+y2,y1+y2+y3} , and y={y1,y2,y3} and m=Array[a,{3,3}]. ...
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1answer
64 views

Partial derivative operator from 2 variables multiplied by functions

My main issue when I try to put all the equations in Mathematica ,I get different solution from what I expected should be,Epsilon 11,22,12 are functions and multiplied by Their partial derivative ...
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0answers
73 views

Solving 2nd order coupled differential equations using shooting method

I'm trying to solve these two coupled 2nd order differential equations: with the following boundary conditions: where $r_{*}$ is the value of the $r$ at midpoint. I was trying to solve these ...
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1answer
86 views

How to simplify complex Trigonometric expression in mathematica? [closed]

The expression which I need to simplify in mathematica into simplest form ...
5
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1answer
204 views
+50

Asymptotic inversion of ExpIntegralEi function

I'm looking at the small-x and large-x asymptotic expansions of the inverse of exponential integral $E_1$ (https://dlmf.nist.gov/6.2#E1) $$\begin{array}{lll} E_1 & = & \int_z^\infty \frac{e^{-...
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0answers
53 views

Second operator for simple equation [closed]

The second operator for a function in manual solution doesn't work as the same as in the Mathematica wolfram code? what should I modify in the code to give the same as manual solution? ...
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0answers
29 views

How to NSolve when an NIntegrate is involved?

I need to find the set of 3rd order polynomial coefficients that will give a bounded exponential function f(x) = Exp[ c0 + c1x + c2x^2 + c3*x^3] a set of specified 0th,1st,2nd,and 3rd order moments. I ...
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1answer
65 views

Solving integer equation with an oddness (or related) constraint

Consider this problem: Find all $x,y \in \mathbb{N}$ with $\{ x,y \} \leq 100$, $y$ is odd, and $$\frac{1}{x} + \frac{4}{y} = \frac{1}{12} .$$ One can convert the condition on $y$ to be $y = 2 z + 1$ ...
5
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1answer
187 views

Problem with NDSolveValue

I am trying to solve some 3D PDEs (for example, 3D diffusion equation) with step function or DiracDelta function as initial condition. I know those functions have discontinuity so I use some ...
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1answer
49 views

Solving generating conditional expression despite assumptions

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2answers
54 views

Removing transient part in equation and solving for a general form

I have the following code that I run: ...
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1answer
50 views

Write expressions in simpler form with substitution for part of the epxression

I have faced this situation many times where I get values like this as solutions: ...
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1answer
112 views

Setting a function equal to an integral

I am trying to solve for the constant of integration in simple calculus problems. v[t_] := Integrate[-0.08 t, t] + C v[t] gives me ...
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0answers
42 views

Function not evaluating as expected [closed]

I'm not sure I understand why this is not working and why it's giving different answers: A simple example illustrating the issue is below: ...
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1answer
32 views

Solve in parametric equations in term of a set of parameters

I am not sure the title is right but let me explain. I have the relations ...
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0answers
30 views

Solving a determinant to get non-zero roots in a heat transfer problem

I am trying to solve a mathematical model of a heat transfer problem. As an intermediate step there is a characteristic equation in the form of a determinant, which needs to be solved for variable <...
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1answer
53 views

Solving a second-order equation by imposing the constraint that the variables are real

I want to solve this equation $$1 + x + x^2 + y - x y + y^2 = 0$$ under the constraint that both $x$ and $y$ are real (not complex). (Note that the unique solution is $(x,y) = (-1, -1)$.) I first ...
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0answers
45 views

Making Intersection of 3 Lines Calculation More Efficient

So I managed to optimize the calculation a little for looking for 3 line intersections in equally spaced points around a circle by only checking one "wedge" of the circle, ignoring ...
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0answers
44 views

How to set up a boundary condition on the diagonal of a region that restricts a partial derivative?

The problem is to solve the Laplace equation on a polygon with one of the boundary conditions specifying derivative on the boundary. Let us consider a polygon region. ...
5
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1answer
180 views

Airy function zeros, conflict (error?) between Wolfram Functions vs. Mathematica

According to functions.wolfram.com, the zeros of the Airy function $\operatorname{Ai}(z)$ occur at $z_k=f\left(\tfrac{3\pi}{8}(4k-1)\right)$ for $k\in \mathbb{N}$ where $f(d)=-d^{2/3} \left(1 + \frac{...
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1answer
41 views

Reduce coefficients from constraints in a set of equations

Total beginner here. I am chaining 4 quadratic equations $f_i(x)$ at 4 knots $k_i$ (where $0 < k_i < 1$ and $k_{i+1} > k_i$) on a wrapped unit interval (i.e. $0 \leq x \leq 1$): $$ f_i(x) = ...
2
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2answers
85 views

Using `FindRoot` to solve over positive integers?

I need to solve for the smallest positive integer $s$ such that the following is satisfied for $p>1, n\approx \infty, \epsilon>0$ $$\frac{\sum_{i=1}^n \left(1-i^{-p}\right)^si^{-p}}{\sum_{i=1}^n ...
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1answer
49 views

How to force NMinimize to find the correct global minimum for equation with many local minima?

I have a function that I am unable to recover a solution for. Here, 0.533... and 0.428... are the exact solutions for Rs[399] and ...
1
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1answer
75 views

Solving an equation matrix with NDSolve

Imagine I want to solve the following matrix system of equations $$ \begin{pmatrix} \dot{x}_{11} & \dot{x}_{12} & \dot{x}_{13}\\ \dot{x}_{21} & \dot{x}_{22} & \dot{x}_{23}\\ \dot{x}_{...
1
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1answer
120 views

Plotting Intersection Points Between 3+ Lines

For a personal project involving a coordinate system for navigating the galaxy using 36/38 equidistant points around a circle, I need to find all intersections between 3+ lines using 3 pairs of points ...
4
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1answer
96 views

Solve misses positive solutions

Why Solve returns only negative solutions? Let $n \in \mathbb{Z}^{+}$. I want to find geometric position of roots of polynomial $p(x)=(x-1)^{2 n}+(x+1)^{2 n}$ in ...
4
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1answer
126 views

Difference between when Solve returns `{}` and `{{}}` [closed]

I have two Solve commands in Mathematica. The first happens to be a matrix equation (not sure this is relevant, but just in case), and it returns ...
2
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0answers
36 views

What sorts of expressions can be Solve'd for?

We can Solve for expressions that match _Symbol, as in Solve[x^2+1 == 0, x]—but we can also ...
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1answer
59 views

Numerically solve 2nd order differential equations:

I'm trying to solve these two coupled 2nd order differential equations, but I'm getting nowhere. Mathematica can't seem to solve these no matter what I do. The equations are: The $r_{*}$ is the value ...
1
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1answer
40 views

A quadratic system with two solutions which may be solved with numeric coefficients, but not with symbolic ones

The system below may be solved using the observation that the second and third equation admit solution (,0,0,); alternatively, the determinant of these two equations must be 0. ...
2
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3answers
185 views

Solution of a nonlinear equation depending on the parameter

I need to solve an equation Solve[m + x*(-1 + 2*x - Log[2*Pi]) + (-1 + 2*m - 4*x)*x*Log[x] == 0, x] It is not possible on a symbolic level. It would be ideal to ...
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0answers
29 views

Getting the coefficients of an expression with Solve

I have a very lengthy expression (600+ terms) with derivatives of several functions, which I want to write in a compact way. I would like to get the coefficients of terms I know exist in this ...
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1answer
56 views

Finding the absolute value of the roots of a polynomial

So I am trying to find the absolute value of the roots of a polynomial in Mathematica. I am quite new to this software and I am having a hard time how to figure out the absolute value of the roots of ...
3
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1answer
64 views

RSolve solves only one of two equivalent recurrences

I am having an issue with the RSolveValue/RSolve function. Specifically, Mathematica is able to correctly evaluate ...
1
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1answer
60 views

Mass-spring-damper model - Encountered non-numerical value for a derivative at t == 0 [closed]

I'm just trying to solve a single mass-spring-damper-model by this code in Mathematica: ...
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0answers
72 views

help request speeding a code up

I hope everybody is fine at Corona virus times. Can anyone help me in speeding my code up for M=20?Thank you. ...
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2answers
173 views

Is it possible to calculate the desired area analytically?

I have the three two-variable curves $f,g,h$ with $0\leq x\leq \frac {\pi}{2} $ and $0 \leq y \leq \pi$ I use ContourPlot as ...
2
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1answer
75 views

How we can solve heat equation with this particular boundary conditions (error NDsolve)?

Please I need help to solve this heat equation with this particular boundary conditions: This the Code I tried in Mathematica: ...
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1answer
50 views

How solve this system of trigonometric equations?

I have the following system of equations: (substituting any real values for a,b,c,r,Alpha,Beta will return the same answer for x) ...
4
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3answers
220 views

solution of $\frac{1}{x}=\infty$

Is there a way to obtain solution $x=0$ for the equation $\frac{1}{x}=\infty$ in Mathematica? I tried Solve, Reduce, ...
0
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1answer
81 views

Solving a complex equation with Solve

I would like to solve: $e^{-b (1.365)} + e^{-b(-0.350)} + e^{-b(-0.378)} = 0$, where $b$ is complex. So, I have written: ...

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