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

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0
votes
1answer
110 views

How smart is Solve? Figuring out what tricks I should try

I'm trying to solve a large system (~10000) of linear equations using Solve, but the process keeps failing. As-is, I don't know whether it's failing because it's using too much memory or too much time ...
8
votes
4answers
183 views

Combining solutions while solving

Here is a simple representation of my problem. I want to solve Solve[(w^2*c^2 /. #) - 1 == 0, w]& /@ {{c -> 1}, {c -> 2}} ...
2
votes
2answers
257 views

How can I get this sum? [closed]

I want to sum the following numbers. At present I am calculating my sum as follows. a = 10^20 + 10^30 + 10^40; In the above case, if I want to add 100 or more ...
1
vote
1answer
88 views

Applying N to the roots found by Solve gives complex numbers when the roots are real [closed]

I have a function which is f(x) = x^3 - 5 x^2 - x + 1. When I solve for x to find the zeros ...
1
vote
2answers
92 views

How to explain NDSolve that functions must be positive only?

I have a simple system of differential equations to solve but both functions should be positive: x[t] > 0 and y[t] > 0 for all t. I was not able to explain NDSolve this fact so it goes x[t] < 0 ...
1
vote
0answers
67 views

Comparing two ways of fitting systems of ODEs to data

I'd like to ask you if you see any difference between the two following ways of estimating parameters. Given my system of ordinary differential equations that I want to use to find the values of all ...
1
vote
0answers
63 views

Stability region of midpoint method using Solve and RegionPlot

I've been trying to obtain the stability region in the $(\lambda_R, i\lambda_I)$ plane of the midpoint rule $$y_{n+1}= y_{n-1}+2h\dot{y}_n,$$ for the model problem $\dot{y}=\lambda y$. The roots for ...
0
votes
0answers
72 views

Rearranging 5 equations

I am trying to rearrange 5 equations in terms of 5 variables. I have the equations for y1, y2, ...
1
vote
1answer
63 views

How to solve this equation?

Mathematica does not give me the correct solution (-1) for this equation: Solve[9^(x + 4) == 27^(1 - x), x] Do I miss something or is Solve the wrong approach ...
1
vote
1answer
74 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 ...
2
votes
0answers
88 views

Solving a system of two nonlinear equations with many symbolic parameters

I have two nonlinear equations with two unknowns, $x$ and $y$, and many symbolic parameters, $a, b, c, d$. They look someting like: $\frac{1}{x}(1+x)^a (1-b)(cx+dy)=0$ ...
2
votes
1answer
62 views

Find constants in a function? [closed]

Let's say I have a function f[x] with n constants, e.g. f[x] = c1 * x + c2*x^2 + ... + cn *x^n I also have n conditions to find those constants, e.g ...
2
votes
1answer
117 views

Double integral changing the limits

This integral does not evaluate: Integrate[ Integrate[1/(E^((a - c)^2 + (b - c)^2) ), {c, 0, 1}], {b, -Infinity, Infinity}] However, reversing the integrals ...
0
votes
1answer
64 views

How can I resolve the insufficient memory to complete the computation problem for solving function with iterated variables?

I am trying to solve for a value x in a function where the variables varies with iterations of K. Also, there is one variable called "rvsum" which is updated with a certain formula as well. I have ...
1
vote
0answers
78 views

How can I solve an equation where indexed variables get updated during iteration?

I am trying to solve for a root for a certain equation, but some of the variables in this equation are indexed and get updated during iteration. The code that I am interested in is like the following: ...
0
votes
2answers
79 views

Replace $z$ with interpolated function and plotting

I start off with this equation $z(x,y) = sin(xy)$. I create an interpolation from $0 < x < 5$ and $0 < y < 5$. I then use this interpolation on a simple function $w(x,y) = x + y + z(x,y)$ ...
3
votes
1answer
139 views

How to propel the integration of time a little bit further? Numerical solution can not evolve to the max time

I try to solve a nonlinear partial differential equation. I obtain a numerical solution which can not continue to the max time I set, I always receive message NDSolve::ndcf: Repeated convergence ...
10
votes
2answers
644 views

Mathematica isn't sure whether a sum of two positives is positive or not

Mathematica is not able to tell whether a summation of two positive expressions is positive or not. Which is very strange. My three symbolic arguments, $x$, $y$, and $z$, are all real numbers bounded ...
-1
votes
1answer
82 views

Is there a change in V10 with Solve and exponents?

I've encountered a strange problem with V10. I can't quite nail it down, but the Solve seems to be unable to solve equations that it could in previous versions. ...
2
votes
1answer
101 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
207 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
735 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 ...
6
votes
0answers
109 views

FindRoot kills kernel

Bug introduced in 7.0.1 or earlier. Persists through at least 10.0.1. I'm having problems with FindRoot killing the kernel. In my real application, I want to FindRoot on a black-box function ...
1
vote
2answers
79 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
99 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
104 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
200 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
92 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 ...
0
votes
0answers
72 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
149 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
23 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
48 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
103 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
142 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
101 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
78 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
246 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
93 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
51 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
99 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
218 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
115 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
67 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
70 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
279 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
64 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
81 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
59 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
75 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?