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

learn more… | top users | synonyms (5)

2
votes
1answer
141 views

How to figure out whether a nonlinear inequality holds or not

I have an inequality consisted only of seven parameters as follows: $(1 + g)^{-(m+w)}\big[\big\{a+(1-a)(1 + g)^m\big\}(1 + p q)Q - (1 + g)^w \big\{(1 + g)^m (1 + q)-(1-p)q\big\} Q\big] < 0$ ...
5
votes
2answers
266 views

Counting Real roots

I'm interested on how to count the number of real roots of a random polynomials in an instant, how to put the result in a table and how to plot it in a graph.I generated 1 million random polynomials ...
4
votes
7answers
1k views

What is the equation to plot a vertical line?

Please help. Trying to find area between three curves, e^-x, x = 2, y = 1. Can't find out how to plot x = 2. Don't want to use ...
8
votes
0answers
165 views

FindRoot kills kernel

Bug introduced in 7.0.1 or earlier and persists through 10.0.2. Fixed in 10.1.0. I'm having problems with FindRoot killing the kernel. In my real application, I want to FindRoot on a black-box ...
1
vote
2answers
134 views

Solving a two point boundary problem for a piecewise system of equations

I'm trying to solve a two point boundary value problem with a piecewise system of equations like: ...
0
votes
3answers
103 views

How to manipulate with external data?

I have a .txt file which contains a lot of triples (a, b, c) (one per row) which should be coefficients of my equation ax^2+bx+c=0. I want to include each triple in .nb file and solve each equation. ...
-2
votes
1answer
126 views

How can I produce a list of solutions for a function which is updated with updated variables using for loop?

I need to loop over a set of equations, solving for X and adding the new X value to the old X value at each step. The output I need is a list ...
2
votes
2answers
240 views

How do I feed data points into an equation to solve NUMERICALLY?

I start with this equation and solve it numerically for $z(x,y)$ in the range $1 < x < 5$ and $1 < y < 5$: $$ \frac{3}{xyz} - 2x - 3y - 5z = 0 $$ Then using the data points of $z$ above, ...
2
votes
3answers
178 views

Solve equations within range and plot [duplicate]

Hi I have these pair of equations to solve: $$ 1 - 3 x y = 5 z - 2 x $$ $$ y = 7 x z - \frac{z}{x} $$ I want to eliminate $z$ and plot $y(x)$ within the range $-2 < x < 2$ and $-2 < y ...
2
votes
3answers
157 views

When NSolve fails due to a differential situation?

c = 1.1111; y[x_] = x - c Sin[x] NSolve[y[x] == 0, x] The method has procured no result. Successive derivatives were plotted in an attempt to fix the problem. ...
2
votes
2answers
159 views

How can Mathematica help me to find a real radical expression for roots of this polynomial?‎

The polynomial $P(x)=x^‎‏4‏‎-‎‏4‏x^‎‏2‏‎-‎‏2‏x+‎‏1$‏‎ has ‎‏4‏‎ real roots (this can be clearly checked by plotting). But solving $P(x)=‎‏0‏‎$, using ...
0
votes
0answers
75 views

Solving a linear system in three unknowns [duplicate]

solve[{2 x + ay - z, bx - 4 y + z, -x + y} == {10, -30, 20}] $$ \begin{array}{lcr} 2x + a\,y - z & = & 10 \\ b\,x -4y + z & = &-30 \\ -x + y & = & 20 \end{array} $$ ...
2
votes
2answers
163 views

How to obtain a function from a implicit equation?

I have (60 - r/2) (70 - ca - r/2) - (60 - r/2 - ca + (4/25) (70 - r/2 - ca))*(70 - r/2)==0 Reduce[%, {ca}] But How could I obtain directly a function as ca[r_] ...
0
votes
0answers
48 views

System of Nonlinear equations with Gamma and Incomplete Gamma function

The next two nonlinear equations are cumulative ratios of a production system. The mathematical model includes two essential parameters (n, tau) that can be obtained by solving this system. I'm ...
0
votes
0answers
75 views

Using implicit function theorem to examine the relation between variables

I have an implicit function with seven variables defined as follows: $F(g,a,b,c,d,e,f)=2g^5 (1+g)^{-(2+a+b)} \Big(f(c-1)(e-1)(1+g)^a - (d-1)(1+g)^b \big(1+ef+(c-1)(1+f)(1+g)^a\big)\Big)=0$ All ...
2
votes
2answers
357 views

Find roots of a function involving Bessel functions

I'm trying to find the roots of a function involving Bessel functions. Here is my code ...
0
votes
1answer
176 views

Finding real roots for an eigth-degree polynomial

The context for this problem is identical to my first question. Unfortunately my previous result for $L$ was inexact since it was a relatively simple approximation. This time I have managed to produce ...
1
vote
1answer
149 views

NDSolve fails for certain choices of parameters and solve range

I'm trying to solve a pair of coupled ODEs with NDSolve. I know roughly what the solution should look like (both should give periodic functions, pi/2 out of phase, the amplitude of which damp towards ...
1
vote
1answer
108 views

Fitting composed model to experimental data

I have mathematical model based on equation: $y(x) = 1 - \sum_{b=1}^{\inf} 2c_b \sin(c_b x/L) \exp(ax) $ (1), where $c_b$ are the positive roots of equation: $c_b \cot c_b + aL = 0$ (2). $L$ is a ...
7
votes
1answer
281 views

Why does Mathematica not give simple solutions to simple system of equations with powers

I trt to get Mathematica getting me the simple solutions for x and y from this system of two power equations: $$\text{Eq. 1: } z=x^{m}y^{n}$$ $$\text{Eq. 2: }z=\tau x^{m-1}y^{1-n},$$ The simple ...
1
vote
1answer
96 views

How do I link the txt file data sheet to mathematica and extract exact elements that I would like to use in solving for x? [closed]

I am trying to solve for a numerical solution for an equation which contains variables that evolves as index i incrreases. The actual equation that I am using to extract solution for x with an ongoing ...
2
votes
1answer
128 views

Numerically solving systems of (first order) linear delay differential equations

I was wondering, how to solve such a system with mathematica? I found the NDsolve function, but in the reference is not mentioned if it is possible to solve a system of equations.
2
votes
1answer
178 views

Find solutions of equation involving Bessel functions

I'm new in Mathematica and I'm trying to find the solutions of this equation involving Bessel functions $$\eta \frac{ J_{n+1}(\eta a)}{J_n(\eta a)}+\chi \frac{ I_{n+1}(\chi a)}{I_n(\chi a)}=0$$ ...
3
votes
2answers
235 views

What would be the inverse function for the following condition?

I tried the problem but i couldn't take above condition in question in terms of f(x)
1
vote
1answer
137 views

Eliminate z from two equations in x, y, z and plot y as a function of x [closed]

I have this equation to begin with: $$1 - 3 x y = 5 z - 2 x $$ I want to solve this equation for $z(x,y)$, then plug $z(x,y)$ I plug $z$ inside a second equation: $$ y = 7 x z - \frac{z}{x} $$ ...
2
votes
2answers
140 views

Extract data from NDSolveValue result

Okay this is a very newbie question. I have coded a sample problem that solves the heat diffusion equation on an annulus. Here's what I have: ...
2
votes
0answers
110 views

Solving a system of difference equations in an exponential steady-state growth setting

I have a system of difference equations in an exponential steady-state balanced growth setting; all variables grow at the same steady-state rate, say, $g$. I use the notations as follows: Variable $X$ ...
5
votes
2answers
284 views

How to get $x$ in terms of $y$ and $w$ from $w = a p x^{p-1} \left(a x^p+b y^p\right)^{\frac{1}{p}-1}$

I'm having trouble to solve the following equation for $x$ both manually and in Mathematica: $\quad \quad w = a p x^{p-1} \left(a x^p+b y^p\right)^{\frac{1}{p}-1}$ In Mathematica notation: ...
0
votes
0answers
87 views

Symbolically solving a system of nonlinear equations

I am trying to solve the following system of equations and did the following ...
1
vote
1answer
96 views

Find the solution of A^2+AB+B^2 = f(a,b,c) [closed]

I wanted to ask the following question: I need to find the solutions (a particular one is enough!) A and B of the equation $A^2 + AB + B^2 = (a^2+ab+b^2)(c^2+cd+c^2)$ How can I do it? Thank ...
1
vote
1answer
75 views

m equations and n variables. Reducing using Mathematica

I have six equations and thirteen variables. I would like to reduce it to seven free parameters. I used Reduce to solve it but it is taking really long (one full day and no output yet) and I think ...
0
votes
1answer
156 views

How to solve two non-linear equations in two variables [closed]

I am a new user of Mathematica. I have the following non-linear equations in two variables: How can I solve this system with Mathematica?
3
votes
1answer
304 views

Mathematica takes too long to solve this

I have the following system of equations: ...
2
votes
1answer
170 views

How to solve three equations with four unknowns iteratively?

I have three equations of the form $\quad \eta = f(N1L, N2L)$ $\quad N1L = g(\eta, R)$ $\quad N2L = h(\eta, R)$ I want to eliminate $\eta$, so that I can get $N1L$ and $N2L$ for a range of $R$. I ...
3
votes
3answers
140 views

Solving determinant of a Kronecker product of matrices gives a numerical error - why?

I am doing the following steps (code at the end of the post): I start with a 2x2 matrix (smatrix), which is a function of a single variable (u2). I want to set the determinant of this matrix ...
0
votes
0answers
89 views

Using one complicated equation to reduce another

(Relative noob here so don't assume much!) I need to use a vector equation (with $N-1$ entries) in the general form $y_j(x_{i,j},x_{i,j+1},x_{i,j-1})=0, i=1...3, j=1...N-1; x_{i,0}=x_{i,N}=0$, ...
0
votes
0answers
68 views

Making a list of terms ordered by product order

I have some expressions f,g,h that are elements of a symmetric tensor algebra. The expressions are generated by a basis ...
3
votes
2answers
122 views

Trying to solve simultaneous equations based on format found on official website [closed]

$\def\1{x_1}\def\2{x_2}\def\3{x_3}\def\f{f(\1,\2,\3)}\def\bs{\bigskip}\def\b{\begin{pmatrix}}\def\e{ ...
8
votes
3answers
287 views

Is there a relatively quick way to solve my integer-valued equation?

This is a very simple problem. It can be solved by nested Forloops that exhaustively test every possible case, throwing out all non-solutions. Find all the ...
4
votes
1answer
388 views

How to find the integer solution number of a linear system with inequalities?

I have the following system with mixed equality and inequalities defined as: ...
2
votes
0answers
119 views

Error when using EquationTrekker

I just got to know EquationTrakker because I need to do phase graphs for my classes. When I load it ...
0
votes
0answers
78 views

What methods does Solve use?

Could you tell me which method that Solve applies to solve linear and polynomials equations?
5
votes
1answer
123 views

NDSolve solution violates initial conditions

I have the following code: ...
8
votes
2answers
311 views

How can I only draw outer common tangent to two circles?

I have code worked for drawing common tangent lines to two circles(http://en.wikipedia.org/wiki/Tangent_lines_to_circles), now I want to delete the inner common tangent lines, how? ...
7
votes
1answer
206 views

How to find the positive region of this function?

I'm new-ish to Mathematica and I'm using it to learn the basics of derivative trading (for fun not for trading!). I've defined a simple function to calculate the pay off of a trading on a call. I have ...
2
votes
0answers
70 views

How to solve for exponents in an infinite product?

Say I have a power series, $f(x,y) \in 1 + x\mathbb{Z}[[x,y]]$ Then it admits a unique expansion $$f(x,y) = \prod_{i=1}^\infty \prod_{j=0}^\infty (1 - x^i y^j)^{n_{i,j}}$$ for some integers, $i, ...
7
votes
4answers
593 views

Solving $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}+\frac{3 W}{2}$ for $W$

When I solve the aforementioned equation for $W$ or $A$ on Mathematica I get a long and ugly equation in return, namely one of the solutions for $W$ is: (attempt to read at your own health) ...
0
votes
2answers
247 views

Find Root Iteration

I have an iterative sum from $k=0$ to $k=n$ where the resulting sum is a polynomial of degree $n$. I want to find the numerical root of this polynomial using FindRoot, starting from $x_0$ where the ...
4
votes
3answers
170 views

Regarding how to use Reduce

Say for example I am doing the following in Mathematica ...
1
vote
1answer
126 views

Need help solving a system of two 1st order nonlinear differential equations

The original system of equations reads: $\begin{cases} f'(r) + f(r) \left(a(r) - \frac{1}{r}\right) = 0,\\ f^2(r) + a'(r) + \frac{a(r)}{r} - 1 = 0\,, \end{cases}$ with boundary conditions $f(0) = ...