# Tagged Questions

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

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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. ...
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### Setting up a system of equations for solution

There are two lists as follows: ...
161 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 ...
68 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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'...
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### 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 ...
188 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: ...
74 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 ...
157 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 ...
170 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: ...
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### 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: ...
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### 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. <...
133 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.
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### 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: ...
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### 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 ...
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### 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: ...
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### Finding where two parametric paths cross?

I have been looking through other parametric equations questions and am still unsure where to start with this one. I am given two functions: ...
95 views

### Switching between solutions of a fourth order polynomial

I am plotting the roots of a fourth-order polynomial as a function of some parameter $r$ with the following code: ...
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### why is NSolve giving {y,x} in place of {x,y}? [duplicate]

Why is NSolve giving an inverse set of solution? Is it a problem with my computer only? ...
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### How to Solve[] for rational constants?

I am trying to solve a system equations for rational, constant coefficients: ...
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### Find a minimum value which satisfies an equation

I have to find a minimum value of "a" which makes x=-a+b+c, y=-a+b+c^2 positive where a>1, 0 ...
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### Inaccurate answer for a system of equations

When I solve the following system of 6 equations by NSolve, it gives me an answer set; however this answer won't make the 2nd equation equal to zero (i.e. when I put the answers into ...
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### How to find the solutions to $a+b+c+d=60$?

How can I find all the solutions to: $$a+b+c+d=60\quad (0\leq a,b,c,d\leq 30,\; a,b,c,d\in\mathbb N)$$ I've tried to use Solve[], but it says that there are more ...
108 views

### Solving two variable using two expressions each involving summation

I am trying to solve for h1 and h2 using function solve as in below code, Expression in solve has two equation each equates sum ...
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### Complex Polynomial roots [closed]

I have the polynomial $p(z)=1-z^3$, I am using mathematica to get all three roots of $p$, say $a, b$ and $c$, obviously $$1-z^3=(z-a)(z-b)(z-c)$$ However, mathematica gives a wrong answer by saying ...
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### Getting the first solution instance

How do I get Mathematica to stop a solver and give a result as soon as it finds the first solution instance? I tried this: ...
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### Solve not returning anything

I have the following function: ...
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### Sharp Ratio Maximization, Closed Forms

I am trying to get a closed form for the following first order conditions (n=4): Here's the nb-File. The code is as follows: ...
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### Trouble in finding instances of values of variables that satisfy an inequality

Consider the following mathematical expression with complex numbers (phasor) and two variables (lambda and ia2): ...
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### Solving $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$

I would like to solve the following equation: $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$ I have already posted it here, but still it doesn't work for me (I don'...
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### Closed form of two-layer recurrence

I am trying to find a closed-form expression for $A(0)$, described by the following recurrence forms, as a function of $L$ and $d$: \begin{align} A(\ell) &= 1 + 2^d A(\ell+1) + \sum_{g=0}^{d-1} \...
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### Plotting level curves for 2-variable exponential equation (Lotka-Volterra) - how?

I have $$\frac{e^{(d x + b y)}}{x^c y^a}$$ Incidentally, this is the energy integral for Lotka-Volterra as given by my lecturer's notes. I would like to draw the level curves for this equation for ...
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### How much time for solving a system of equations?

I wrote the following code for system of 11 equations; however when I run, it shows "Running" and has not converged to any answer after 2 hours. Please let me know whether it is normal or how I should ...
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### Problem in solving non linear set of equation?

I am trying to solve a set of non linear equation but using the function nsolve but mathematica is not giving me proper answer. The code is given below. ...