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

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3
votes
3answers
171 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 ...
8
votes
3answers
336 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
654 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
171 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
98 views

What methods does Solve use?

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

NDSolve solution violates initial conditions

I have the following code: ...
9
votes
2answers
360 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
290 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
77 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
734 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
385 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
194 views

Regarding how to use Reduce

Say for example I am doing the following in Mathematica ...
1
vote
2answers
216 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
213 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 $\beta \in [0,\pi]$: ...
9
votes
4answers
761 views

How many times do the two given curves intersect at the origin?

I'm reading/studying on my own a book about algebraic curves. I'm trying to find a way for Mathematica help me with the following (the book, ISBN: 038731802X, allows me to use any CAS / program. ...
3
votes
1answer
273 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
110 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 ...
0
votes
2answers
85 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 $Abs[\Gamma]$ ? ...
1
vote
0answers
187 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
165 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
136 views

Quartic equation [closed]

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
1answer
741 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
203 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
58 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
246 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
100 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
351 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
416 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
91 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 ...
12
votes
2answers
399 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
38 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, ...
3
votes
1answer
716 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
129 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
115 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
60 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
34 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
114 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
1answer
150 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, ...
1
vote
1answer
139 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
64 views

Some question on “Reduce”

Is this my mistake? I am trying to solve ...
3
votes
1answer
74 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
60 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
178 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
66 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. ...
1
vote
1answer
187 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
84 views

Solve gives a solution which is contradicted by an example

I have the problem as described in the title. Here is the code: ...
1
vote
3answers
741 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 ...
6
votes
2answers
348 views

NSolve missing solutions in Mathematica 10

Running Mathematica 8.0.4 and 10.0.0 on a Windows 8.1 machine. Processed the same code with both kernels: ...
13
votes
5answers
1k views

Solve symbolically a transcendental trigonometric equation and plot its solutions

I currently have the equation below for a beam with a hinge at various locations, the variable a can vary between 0 and 0.5. $$ Tan\left( {a\sqrt \alpha } \right) + Tan\left\{ {\left( {1 - a} ...
0
votes
1answer
95 views

A problem with “RiccatiSolve::ncsol: Cannot compute a stabilizing solution to the matrix equation ”

I have a SSM ( State Space Model ) and I want to calculate its optimum gains unisng LQOutputRegulatorGains[] command. When I run the code, it solves the equations ...