# Tagged Questions

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

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### Solve problem: Inconsistent or redundant transcendental equation

I would like to mechanically Solve[a y == (1 - a) x && u0 == x^a y^(1 - a),{x,y}], given 1>a>0 and u0>0. The emphasis is on mechanically: I know it is ...
160 views

### How to find an estimated root efficiently with binary stochastic estimation of the function?

I am trying to construct certain nice geometric patterns, and one particular feature I'm trying to optimize is the balance of black and white corresponding to point being inside, or outside a ...
53 views

### Generic approaches for multivariable polynomials across different domains [closed]

Mathematica newbie here. So I don't have a lot of time to read through the whole library of functions and language rules. So I'm trying to settle in on generic ways of doing the math that I'm going to ...
278 views

### Can I solve a certain equation?

Neither Mathematica nor Wolfram|Alpha can resolve the following. How else can I reach a solution? Reduce[(1 + x)^(2/m) - (1 - x)^(2/m) == (1 - x^2)^(1/m), x]
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### How to solve an equation given certain parameters?

I am new to Mathematica so please bear with me. I have an equation that has around 7 parameters and one unknown. I was able to use FindRoot to solve it; however, I ...
212 views

### Plotting results from Findroot

I know this has been asked, but I cannot seem to understand the solutions. What I need to know, because I have my first domiciliary test this Monday, is how to plot the output from ...
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### Find all degenerate eigenvalues of a cubic equation

I have an equation that is cubic in w. The three solutions correspond to bands in a bandstructure, and are a function of wavevector ...
205 views

### Re-parameterizing sections of a Bézier curve into normal Cartesian functions [closed]

I have a table: ...
189 views

### solving system of non-homogeneous advection equation using mathematica?

This question is followed up from this question How to solve a certain coupled first order PDE system Here I consider the non-homogeneous advection system \displaystyle\left\{\...
227 views

### NSolve erroneously gives no solution to a polynomial system

I have a polynomial system with three equations in three unknowns, the maximum degree is 26. Two equations are symmetric, i.e. eq1(x,y,z)=eq2(y,x,z). If I search ...
249 views

### How to solve a certain coupled first order PDE system

I would like to find the solution $(U,V)\equiv (U(x,t),V(x,t))$ of the following system. \displaystyle\left\{\begin{array}{l} \frac{\partial U}{\partial t}+(a+b x)\frac{\partial U}{\...
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### Solve a transcendental equation in Mathemathica

I believe it is called a "transcendental equation", and I would like to find the best possible sollution. I tried to use Solve: ...
189 views

### Finding closest point to implicitly defined curve

I'm facing the following problem: Given an implicit curve given by $f(x,y)=0$ and an initial guess $(x_0,y_0)$ which is hopefully close to the curve, I want to find the point $(x,y)$ on the curve ...
583 views

### Solving a transcendental equation

I want to solve the a transcendental equation, e.g. NSolve[-(1-x)*Log[1-x] - x*Log[x] == 0.5, x] Mathematica is not able to solve, wheres WolframAlpha -- is able ...
88 views

### Reduce Inequality

How can I reduce the inequality in terms of modulus of alpha. ...
176 views

### How to solve a nonlinear overdetermined system of equations

i'm trying to solve a nonlinear overdetermined system of equations (124 equations, 123 variables) i tried this procedure (newton raphson) ...
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### Finding the conditions for degenerate solutions to a cubic equation

I have a cubic equation (corresponding to the band structure of a physical system) given by w in the code below. ...
86 views

### Setting up a system of equations for solution

There are two lists as follows: ...
159 views

### Solving a system of weird equations

I'm trying to have Mathematica solve a system of equations for a friend's work in Computer Vision. I'm essentially going in blind to this and am not very familiar with Mathematica syntax, so would ...
67 views

### Removing imaginary and negative results from Solve

I have been trying to solve a series of equations that I know have real positive values for the unknowns (they all have real world analogues and they are not linked to a frequency domain) but despite ...
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I am trying to solve a system of differential equations. ...
69 views

### NSolve not solving [closed]

I've been working on a Newton Cooling equation problem for my diff equ class and cannot get NSolve to solve this equation. I've plugged it into Wolfram Alpha and my ...
76 views

### Using result of Solve in further calculations

I'm trying to make a code for Gauss-Legendre quadrature. First I find the roots of the polyinomial with roots[n_,x_]:=Solve[LegendreP[n, x] == 0] Then I need to ...
97 views

### Solving non-linear ODE analytically in mathematica [closed]

I would like to solve the following differential equations $${dx\over dt}=\beta x-{{(C-x)^2}\over 4k} ,t\in[0, T]$$ where $\beta$,$C$ and $k$ are constant values. Also, the folowing terminal ...
1k views

### Does Mathematica have a built-in tool that allows one to operate on both sides of an equation?

Geogebra has a very neat CAS view that allows one to solve an equation step by step in the following fashion: $\quad \quad \quad \quad \quad \quad \quad \quad \quad$ You type an equation and ...
96 views

### Reduce with for all and implies

I have the following question. p1 = a (1 - c + a) p2 = b (1 - c - b)/((1 - b)^2) v1 = (x^1.5 - 3*x)*p1 v2 = x*p2 I want to find x ranges which makes v1>v2 under ...
565 views

### Solve a trig equation system

Background of the problem In the same plane, P is a fixed point, A,B,C are moving point, PA=a, PB=b, PC=c, find the maximize perimeter of △ABC. let ∠BPC=A, ∠CPA=B, ∠APB=2*Pi-A-B, then the perimeter ...
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### Why does NSolve not solve this system of equations on a bounded domain? [duplicate]

I have three functions $E1,E2,E3$ of $t1$ and $t2$. The expressions are slightly complicated and involve trigonometric functions. For clarity purpose, they are given at the end of the question. I wan'...
253 views

### Find all roots of a function with parabolic cylinder functions in a range of the variable

I want to find all roots of a function involving Parabolic Cylinder Functions. In what follows, I define 2 variables $\xi1$ and $\xi2$, which in turn depend on $\omega$. My function is then defined as ...
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### What is the role of the pattern object in this implementation?

In the documentation I found a nice idiom which allows me to do model fitting with interpolating functions. I think this kind of thing is amazing and a credit to the utility of an environment like ...
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### How can I solve an equation independent of a variable? [duplicate]

Let's say I have the equation $$ax + b = 0$$ and I'd like to find a solution that doesn't depend on $x$, so here the solution is obviously $a=b=0$. I could solve this using ...
186 views

### How to properly interpret a seemingly contradictory result in Mathematica?

I have a problem with interpreting the results of my notebook outputs. It is important that I do not err with the interpretation. Here is the full input: ...
72 views

### Problem with plotting a function that calls FindRoot [closed]

I am having difficulties in plotting the solution of FindRoot to solve 4 variables. I defined a function and then tried tp plot it, but got an error message ...
154 views

### Solve returns empty list / running forever

Update: I made a mistake before and corrected the sign in code below in case people wonder what some comments mean. Thank you for those who answered. But I should have said that this is only part of ...
164 views

### Why does Mathematica not evaluate the difference recurrence using RSolve or RecurrenceTable?

Mathematica does not evaluate the following recurrence of two variables using RSolve and only echoes the input: ...
138 views

### How to find zeros of 16th degree polynomial with coefficients which contain one symbolic parameter?

I'm trying to find eigenvalues of matrix which is 16x16. Here is a part of matrix: ...
79 views

### Inverse Superposition

There are 4 tables that, I have written them as bellow: (m, n, s, and r are orthogonal basis. r.r=n.n=m.m=s.s=1, and m.n=n.r=...=0). a's, b's, c's and d's are coefficients and are numeric values. <...
132 views

### Solve[ ] doesn't work with transcendental equations

How to solve x^5-sinx=0 in mathematica? I try in this way: Solve[x^5 - Sin[x] == 0, x],but t doesn't work.
200 views

### How can I find all solutions of a complicated expression in a desired interval with Mathematica?

I have an expression which is a combination of Bessel functions: ...
136 views

### Problems with finding the real solutions of equation

I am trying to find real solutions of equation using Mathematica 8.0 but there is some problem I don't know how to explain. For example, for the input ...
56 views

### Unexpected ReplaceAll behavior with NSolve

I ran into some unexpected behavior using ReplaceAll with an equation of motion using NSolve (or Solve, also). First solving for the initial velocity v0: ...
I am plotting the roots of a fourth-order polynomial as a function of some parameter $r$ with the following code: ...