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

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5
votes
3answers
168 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
90 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 ...
3
votes
3answers
119 views

Regarding how to use Reduce

Say for example I am doing the following in Mathematica ...
1
vote
1answer
86 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
76 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
47 views

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

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
35 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
131 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
86 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
41 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
64 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
24 views

Add condition for all variables in list to $Assumptions, to use with Reduce [closed]

I want to reduce a non-linear system of 26 equations using Reduce, more precisely the following command ...
0
votes
0answers
59 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
1answer
133 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
95 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
79 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
52 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. ...
0
votes
1answer
51 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
37 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
31 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
224 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
87 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
157 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
4answers
131 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
47 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
42 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 ...
10
votes
2answers
269 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
30 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
45 views

NDSolve solution methods issue

I´m modelling a biological reaction thorugh a set of differential equations. ...
3
votes
1answer
178 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... ...
0
votes
2answers
101 views

Solving an Equation (Recursively)

I have the following Values: $a[0]=1;a[1]=0;a[2]=0;a[3]=0;a[4]=\frac{g_2}{20};a[5]=0$. I need to compute the value of $b[n]$ in the following equation $$a[n]=\sum _{m=0}^{n} (m-2) \;\;a[m] ...
1
vote
1answer
86 views

How do I solve for the real and complex parts of an equation simultaneously?

If I were to have an equation, say something similar to... (1-Sqrt[x - I y])/(1+Sqrt[x - I y]) = A + I B Where I = Sqrt[-1], is there a way for Mathematica to ...
0
votes
1answer
56 views

Why can NSolve only solve this system of equations after trivial substitution?

The first system immediately yields {}, but the second, equivalent, system yields the solution {{k -> 4.96048, tl1 -> 1.64842, tl2 -> 2.07466}} : ...
0
votes
0answers
29 views

What is that Root[…] inside the answer represent? [duplicate]

So I am encountering this situation, in which mathematica doesn't give me the answer, but in a form of "Root". How do I interpret this ? what is the number after the "&" represent? How should I ...
2
votes
0answers
67 views

How to handle infeasible points in FindRoot?

I am calling FindRoot[f[x,y],{{x,xInit,xMin,xMax},{y,yInit,yMin,yMax}}] where for some points {x,y}, ...
0
votes
0answers
46 views

Finding Roots of Non-linear Systems: Rescaling polynomials

I'm trying to get all isolated finite equilibria of a moderate multi-dimensional non-linear system of equations. Particularly I have 9 independent variables and third order at most. It turns out that, ...
0
votes
0answers
97 views

NSolve for large models

I'm a Mathematica rookie running version 7.0 for Mac OS X x86 (64-bit) (February 19, 2009) on a 2010 MacBook Pro. (I'm also a stackexchange "newbie" who originally posted this on stackoverflow, thus ...
0
votes
1answer
47 views

Simplifying a symbolic product of rational powers

I'm trying to symbolically evaluate a lot of equations that can consist of up to 10 parameters. The form of these expressions is a product/quotient of rational powers of the mentioned parameters, ...
0
votes
1answer
41 views

How to use an output of a Solve function in further calculations? [closed]

Following is the polynomial equation that gives me a single real root: ...
1
vote
1answer
49 views

Numerically Integrating to find a Maximum using NDSolve

I am trying to numerically find an equilibrium (maximum) of a function using its differential. The following is a simplified version. ...
1
vote
1answer
55 views

Some question on “Reduce”

Is this my mistake? I am trying to solve ...
3
votes
1answer
56 views

Finding linearly independent combination of vectors with a certain symmetry property

I have two linearly independent vectors $v_1$ and $v_2$. Is there a way for me using Mathematica to find two linear combinations $w_1$ and $w_2$ such that: $w_1$ and $w_2$ are linearly independent. ...
1
vote
1answer
51 views

Can someone please help me to state assumption?

I am currently trying to solve under what condition does the following term will be zero? ...
3
votes
1answer
84 views

Aborts and beeps without error warning

I have a piece of code that generates a figure, performing a calculation to generate each pixel. At a certain resolution it runs fine, but after a high enough resolution it fails. Mathematica beeps ...
0
votes
2answers
54 views

Eigenvectors inside a maniupulate function

I am trying to make a physics application and it requires that the eigenvectors be taken for a 3x3 matrix. It is my intention that Mathematica never have to deal with the matrices symbolically. ...
0
votes
0answers
33 views

Replace parameter of NDSolve by a Function

I dont know how to replace the paremeter inside of an interpolation function result from NDSolve by a function of another parameter. This is it: I have a ...
2
votes
1answer
94 views

Mathematica unable to solve equation numerically while Wolfram|Alpha can

I want to solve the following equation 2 x == Sinh[x] Mathematica is unable to do so ...
1
vote
2answers
72 views

Solve gives a solution which is contradicted by an example

I have the problem as described in the title. Here is the code: ...
0
votes
0answers
46 views

Calibrating a difference equation system

Sorry for not posting it in the first attempt properly. Consider the simple problem of a first-oder difference equation: ...
1
vote
3answers
163 views

Mathematica Solve function does not solve double exponential

I am trying to solve: Exp[-a Exp[-x/b] - c Exp[-x/d]] == Y to x, and using the command ...