Tagged Questions

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

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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
72 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
65 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
60 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
76 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
151 views

Mathematica takes too long to solve this

I have the following system of equations: ...
2
votes
1answer
129 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
117 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
73 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
60 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
92 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
252 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
179 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
61 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
54 views

What methods does Solve use?

Could you tell me which method that Solve applies to solve linear and polynomials equations?
5
votes
1answer
101 views
8
votes
2answers
254 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
145 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
59 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
388 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
136 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
141 views

Regarding how to use Reduce

Say for example I am doing the following in Mathematica ...
1
vote
1answer
100 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) = ...
4
votes
2answers
93 views

Can't solve equation having complex coefficients

Why can't Mathematica solve $\quad\quad\frac{1-i}{\sqrt{2}}=e^{i \alpha } \tan \left(\frac{\beta }{2}\right)$ with the restrictions $\alpha \in [0, 2 \, \pi)$ and $\beta \in [0,\pi]$: ...
0
votes
1answer
50 views

How to find the value of a solution of an ODE at a particular point [closed]

I'm trying to find the value of $z(y)$ at a particular time, say $y=0.5$. I've solved the differential equation. I tried using z3 = z[3] /. sol, but it's not ...
0
votes
0answers
40 views

Difficult to solve the equation using FindInstance and not able to solve it numerically

I hope to find the range of a which leads to non-zero solution of H when you are given a specific value of B. And I hope to get ...
3
votes
1answer
162 views

Issue in ParallelTable after evaluating another function using NDSolve and FindRoot. What is wrong with this inverse?

I am trying to find the inverse of a function which is defined through NDSolve and NIntegrate. The question is pretty similar ...
3
votes
1answer
96 views

Already solved DE, now I need to rearrange and plot

I have solved for $z(w,x,y)$ in a differential equation: $$ 3\frac{\partial z}{\partial y} = 2(z-1) + (1-wy^2 )x $$ And I obtained the general solution: $z = f(w,x,y)$ Now putting in $x=0$, we have ...
1
vote
1answer
55 views

Solved the differential equation, how to rearrange to find solution? [closed]

I have solved for values of $y(x)$ from $1 < x < 2$ and plotted them: ...
0
votes
2answers
69 views

Solve simple differential equation - Error?

I get the error "The function Te appears with no arguments." when running this code. I'm not sure why. Is it because of the $Abs[\Gamma]$ ? ...
0
votes
0answers
74 views

Best way to determine polynomial coefficients in series expansion

I would like to solve the equation $$h'(\boldsymbol{x}_1)\left[B_1\boldsymbol{x}_1+g_1(\boldsymbol{x_1},h(\boldsymbol{x}_1))\right]=B_2h(\boldsymbol{x}_1)+g_2(\boldsymbol{x}_1,h(\boldsymbol{x}_1))$$ ...
0
votes
0answers
145 views

Could not solve a set of equations with available mathematica tools

The problem I described below is an simplified way of expressing it.(Sorry that I still did not figure out a way to copy the code to here.) The actual equation is like What I am trying to find is ...
0
votes
1answer
150 views

Solving a Trigonometric parameter

I have a similar case as given before : Solving a Trigonometric function with one parameter Let: m = 1; Dx = 100; ν = 0.25; b = 1; and, ...
2
votes
0answers
82 views

Quartic equation

After using Solve I am choosing the physical root of my equation and dealing further with this root. However, when I am changing parameters using Manipulate, I clearly see not smooth behaviour. Is ...
0
votes
0answers
85 views

Using Solve but getting no output

I am trying to solve a model using a constant-elasticity-of-substitution production function, but when I try to solve the first order conditions, I just keep getting back what I typed. ...
1
vote
1answer
82 views

Solving equations with QuantityVariable

I'm trying to understand how to easily solve equations that use QuantityVariable. Why does this fail? ...
0
votes
0answers
38 views

Step by step solution of an equation [duplicate]

How I solve this system of equations STEP BY STEP in mahematica. \begin{align} (x + 1)^2 [(p - l)^2 + (q - m)^2] &= (a - l)^2 + (b - m)^2 \\ (x + 1)^2 [(p - a)^2 + (q - b)^2] &= x^2[(a - l)^2 ...
0
votes
0answers
39 views

Resources/ best practices for exploratory economic theory work

This is a little general, so I will try to make it as specific as possible. I used Mathematica a fair amount to derive and check analytical solutions to problems in theoretical economics. Lots of ...
1
vote
2answers
230 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 ...
1
vote
1answer
91 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 ...
1
vote
4answers
174 views

How to extract only real solutions from the result of Solve

For Example, I have the following polynomial equations: $$ \left\{ \begin{array}{ll} \dfrac{2025 (208 x+5 (y-3446))}{52 (y+90)^2}+\dfrac{300 (8 x-21 y+1920) (y-80)}{7 (x+30)^3}+\frac{300 (80 x-21 ...
1
vote
3answers
173 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 $z_{max}(x,y)$ ...
0
votes
1answer
55 views

Solving minimum length confidence interval problem

I'm trying to find the minimum length of a confidence interval for the variance from a sample iid with normal distribution. I tried ...
1
vote
1answer
47 views

How to get only the real solutions of an equation? [closed]

Is there any simple way to get only the real solutions of the eq. x^3-1=x? I've tried: Solve[x^3-1==x,x] But it gives the complex ones, too. I have Mathematica ...
11
votes
2answers
306 views

Solving the magic backyard puzzle with MMA

I was trying to solve this puzzle using mma It looks like the generalization of the magic square. Anyway here my attempt:- There are four columns $(x,y,z,w)$ and nine rowa which are denoted by the ...
0
votes
0answers
32 views

How can Mathematica solve 7 equations and want to find 7 variables [duplicate]

I have 7 equations as below * e1 := (1 - a) p Subscript[A, 0] Subscript[s, K ] ! *SubsuperscriptBox[(s), (L), (-a)] = (1 - b) Subscript[B, 0] (1 - Subscript[s, K]) (1 - Subscript[s, ...
-1
votes
1answer
57 views

NDSolve solution methods issue

I´m modelling a biological reaction thorugh a set of differential equations. ...
3
votes
1answer
242 views

How do I solve for one variable in terms of other variables in Mathematica?

I'm fairly new to Mathematica, and I'm trying to solve a complicated equation with multiple variables. I've tried the following... ...