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

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Conditional expression

How do I evaluate a conditional expression in order to convert the solutions that are in terms of $x$ to a new variable $c$ depending on $x$? The conventional method I have been using with eliminate ...
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3answers
76 views

Finding roots of transcendental equation and collecting into a list

I am working on a physics reserach project for school and I have run into some troubles working Mathematica. I am a fairly inexperienced mathematica user so any help would very much be appreciated. I ...
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2answers
112 views

Solving for the limits of an integral

I am trying to get Mathematica to solve for the symmetric limits of an integral of a Square Wave. ...
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2answers
112 views

Why does this expression take a long time to evaluate?

I was just wondering whether there's an easy to see reason for this expression to take a very long time to evaluate: ...
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1answer
134 views

FindMinimum and NMinimize to solve equations

I know that I'm not a Jedi in solving Equations and minimizing functions; but now I've this problem, and the solution is far to me. I want to solve this equation: ...
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1answer
122 views

Unexpected result from FullSimplify

In the following simplification why doesn't Mathematica get a zero when asked to compute "Y-Z" eventually? ...
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2answers
646 views

Solve within a range?

Is it possible to solve an equation in which some some of the parameters have defined ranges? Example: ...
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2answers
442 views

Projection of curve 3D (x,y,z) on the x-y plane

I have a following systeme : \begin{equation} \left\{ \begin{array}{rcr} (\beta+\frac{1}{2}\delta^{2})\nu_{1}(u)-\delta\nu_{2}(u)+\nu_{3}(u)& = &0\\ ...
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1answer
206 views

Help to solve exponential equation over positive integers

I am trying to solve the equation $\frac{4}{9} = \big( \frac{1}{3} \big) ^n + \big( \frac{1}{3} \big) ^m $ with $n$ and $m$ both positive integers. I type into Mathematica the following In:= ...
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3answers
150 views

automatic processing of numerical results in `Plot`

First I want to solve an equation $F(x,y)=0$ for $y$ by supplying a value of $x$. (suppose obtaining the analytic form of $y(x)$ is too difficult) Then I want to plot root $y$ (numerically calculated) ...
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1answer
444 views

Substituting solution from Solve into the equation and making a plot

I want to solve an equation and substitute it into a Plot expression. My code looks something like this a[b_, x_] := bx + 1; sol = Solve[(1 + b)x + 1 == 0, b] I ...
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3answers
3k views

How can I use assumptions with FindRoot?

I have something like FindRoot[f[x], {x, a}] Now I want FindRoot to constrain the solutions to 0 < x < 1. How can I ...
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1answer
554 views

Comparing two symbolic expressions

Does Mathematica provide any way to compare two symbolic expressions and find which is the greatest? For example, I want to find which is the greatest of ...
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2answers
445 views

Replacing variable in an equation with an Interpolating function polynomial and plotting residual

I was trying to plot the residual for the solution of my PDE. However, I was unsure about a couple of things. I imported the data and created an Interpolation polynomial with ...
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1answer
846 views

FindRoot inside Table

(MWE at the end of the post) I need to solve a non-linear equation $f(y;x_1,x_2,..,x_5)$ in one variable $y$ and then compute 4 new output expressions, for over 60 different initial parameter inputs ...
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1answer
72 views

Improving Performance - Finding Polynomial Roots [duplicate]

I'm fairly new to Mathematica. In the past, my usage has mostly been limited to solving the occasional equation, making some plots, and working with small scaled statistics. None of these have been ...
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1answer
189 views

NSolve fails to solve a nonlinear equation

Mathematica can not solve this: g = 9.82; ω = 0.5; h = 5; y0 = 1; v = 0; τ = 0; NSolve[h + v t - (g t^2)/2 == y0 Sin[ω t], t]; The error code is: ...
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1answer
192 views

solve recursion equation with condition

How can I find $f(x)$ in terms of $x$ in the following equation? $ -k\, x \,f(x) + k \, (x + 1)\, f(x + 1) - r \, f(x) + r\, f(x - 1) =0$ $r$ and $k$ are constants and $f(x)$ should satisfy: ...
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2answers
120 views

Problems with Solve when constraining solutions to a range

I have the following code ...
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1answer
96 views

How To Replace $\rightarrow$ by $==$ in Mathematica's Output when using Solve

I want to create equations out of the output (solutions) produced by Mathematica when using the Solve functions. For argument's sake, consider the following. ...
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1answer
93 views

Solve for values which produce negative real Eigenvalues?

Given an n x n matrix "A", with one or more unknown parameters, I'd like to show a plot of which values produce stability (negative Eigenvalues). For example, say you have a simple mass-spring-damper ...
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2answers
118 views

How to solve ArcSinh equation for many differents parameters?

I am totally stuck trying to solve the equation below (1/2) x Sqrt[1 + 4 a^2 x^2] + ArcSinh[2 a x]/(4 a) == d Where a and ...
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3answers
114 views

Can I find constants in a function?

Let's say, I have a function with a constant, e.g. $y(x)=x+c$, and a condition $y(0) = 5$. I want to type in something like Solve[{y[x]=x+c, y[0] =5}, {c}] and get ...
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2answers
240 views

How do I plot the differential of this function?

Suppose I have this function: $$z(x,y) = \left| \frac{ \frac{1}{3x +iy} -2x}{iy + \frac{1}{x}} \right| $$ I want the contour plot of $\frac{\partial z}{\partial x}$ with axes $(x,y)$. Tried this ...
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1answer
94 views

Whats the most efficient way to solve an equation numericaly (because it has no analitical solution)

So, I think the problem that Im having is simple but, still, Im not sure on how to do it. I have an equation with no analitical solution: $a_1 \sin \left(2 \theta \right)+a_2 \sin \left(2 ...
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3answers
250 views

Finding maximum value with position from Table of values

I have this table of values, how do I find the maximum value? i.e. find $z_{max}(x,y)$ ...
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1answer
197 views

LinearSolve failing to find solution to system of linear equations of 64 variables

I've got a 64x64 Matrix L for which I want to find the solution to the matrix equation L . x == rho. L is defined as ...
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1answer
180 views

FindRoot with vector functions

I'm trying to solve a system of non-linear equations with FindRoot, and I get the answer, but also a ...
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2answers
210 views

NSolve for high degree univariate polynomials

I am trying to solve a high degree univariate polynomial using Mathematica's NSolve command. But when I plug the solutions generated by Mathematica back to the equations, the equations are massive ...
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1answer
257 views

Get Cos[2 x] in “Solve”

My goal is to get an analytical solution of x ( $\lambda$ in the problem), when $\epsilon$ (f[x] in the problem) is maximum (use inverse form). I found that if I can use trigonometric identity ...
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1answer
360 views

How do I get all possible solutions in an underdetermined system? [duplicate]

I have two problems which I'd like to solve with Mathematica. If I have a system of two equations with three unknowns, how can I get to list all possible solutions for the unknowns? Here is what I ...
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3answers
925 views

Solve for variable in integral limit when using NIntegrate

I am trying to solve for a variable which appears in the limits of an integral, rather like in the following; ...
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1answer
226 views

Mathematica Solve Hangs Indefinitely

The following code hangs ...
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3answers
138 views

Discrete inequality plotting

I have an equation like this: $${20 \choose k}\cdot \sum_{i=0}^k {k \choose i}\cdot i \leq 1+f$$. I want to plot this inequality as the dependency between k and ...
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1answer
273 views

General form of a linear transformation

Let $v_1 = \begin{bmatrix} 2 \\ -1 \end{bmatrix}$ and $v_2=\begin{bmatrix} 1 \\ -1 \end{bmatrix}$ and let $A= \begin{bmatrix} 3 & 2 \\ -2 & 1 \end{bmatrix}$ be a matrix for $T\colon \Bbb ...
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2answers
160 views

ReplaceAll a list of rules to an equation

Given the following equation and rule, how would I Solve the equation for tr, k and ...
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2answers
296 views

Approximate solution to system of polynomial equations

I'd like to solve approximately the following system of equations for $a_1$, $a_2$, $\alpha_1$ and $\alpha_2$ all real and nonzero: ...
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1answer
463 views

NSolve cannot solve system of equations in Mathematica

I have the following two equations: ...
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2answers
417 views

Finding shortest non-zero vector $x$ satisfying $Ax=0 \pmod q$

Let $n$, $m$, and $q$ be positive integers (with $m > n$), and $A$ be a matrix over $\mathbb{Z}_q^{n \times m}$. Using Mathematica, I want to find the shortest non-zero vectors $x \in ...
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1answer
370 views

Solving Intervals

In a recent question I posed, it was noted that by design, Sqrt[ blah] only returns the positive branch, even though we might want to obtain all possible symbolic solutions. So, taking care to avoid ...
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1answer
576 views

Graph and manipulate DSolve result

Given a DSolve example: ...
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3answers
2k views

Tricks for solving (lots of) coupled nonlinear equations numerically?

I have a system of 6 non-linear (quadratic) coupled equations with 6 complex unknowns \begin{align*} |x_1|^2 + |x_2|^2 + |x_3|^2 &= a\\ x_1 x_4^* + x_3 x_5^* &= b + c i\\ x_1 ...
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2answers
2k views

Find the dimensions of a cylindrical can that will minimize the cost of the material

A cylindrical can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can. This is a standard calculus problem. The volume of the ...
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1answer
57 views

Characterising the set of parameters that satisfy a system of non-linear equations

I am looking for a solution to the following problem and could not find an answer so far. I have a quintic equation, $f(x;a,b,c,\cdots)-x=0$, where $x$ is the variable with respect to which I need the ...
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1answer
165 views

Solving systems of equations

So I have a set of equations like 12 of them but 13 variables. However I would like to find the numerical value of the roots for the maximum value of a particular variable. I don't know how to do that ...
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1answer
110 views

NSolve for complicated equation involving double cross product

I have the following issue. I am trying to solve a 3-vector equation for the vector slx, sly, and ...
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2answers
113 views

FindRoot: getting number of iteration [closed]

I'm using FindRoot to solve a nonlinear system. I'd like to see what FindRoot is doing while computation, something like the display option for Matlab fsolve. At the end of the day, I want the number ...
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1answer
70 views

Solve never terminates with simultaneous equation set

I have the following set of simultaneous equations that I want to solve symbolically. The two unknowns are $a$ and $d$. $a=\frac{c*(d/10)}{1 + (f/130) + (d/50)} - \frac{a}{1 + (a/100) + (d/100) + ...
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2answers
361 views

Equating coefficients in a non-power-series equation

How can I use Mathematica to equate coefficients in a non-power-series equation? For example, I would like to take an equation like the following: ...
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2answers
157 views

Symbolic matrix equation

I am looking to a system of equations of the form $\pi =\pi P$, the one encountered in Markov chain theory. My $P$ variable is: ...