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

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5
votes
2answers
322 views

Optimum number of cog teeth for two step helical gearbox

Note: Cross-posted at http://community.wolfram.com/groups/-/m/t/137895?p_p_auth=8QnKtT9I. I am to design a two step gearbox. The first step is to choose the number of teeth in each cog wheel in ...
0
votes
1answer
484 views

How can I solve a set of non-linear equations?

I was wondering whether someone can give me an idea on how I can solve a set of non-linear equations with an unknown exponent This is what I have: Known values: N, R Unknown values: λ, α, J ...
4
votes
3answers
442 views

How can I get the exact solution of this equation (inequality equation)?

I want to solve the equation and inequality equation $$\sqrt{8\cdot 16^x - \dfrac{1}{2}\cdot 9^x }= 3\cdot 4^x - 3^x$$ and $$\sqrt{8\cdot 16^x - \dfrac{1}{2}\cdot 9^x } \leqslant 3\cdot 4^x - 3^x.$$ ...
5
votes
1answer
321 views

Use Pattern with Vectors in Assumptions

I had a problem using Pattern with Vectors in Assumptions. Here's how I use ...
0
votes
2answers
628 views

Classification of a linear system of equations with a parameter

I need to get every possible value of k that returns infinite number of solutions or no solution to this system: ...
2
votes
4answers
401 views

find the number of integral solutions a+b+c+d+e+f = 18 [duplicate]

Find the number of integral solutions of a + b + c + d + e + f = 18 where a, b, c, d, e, f are elements of the range ...
4
votes
2answers
333 views

Find the value of parameter so that the equation has one solution

Let $(E_l) : x^4-4x^3+x^2(5-l^2)+4 x l^2-4l^2 = 0$ be an equation with $l$ as a parameter and $x$ as an unknown and $S_l$ the set containing all the real solutions of $(E_l)$. Then there is a unique ...
3
votes
1answer
324 views

How to find the roots of an equation which is almost singular everywhere

I'm trying to find the roots of the equation as a variable of k: ...
2
votes
0answers
125 views

Equation Solving: Solution in terms of predefined functions

Is there a way that I can have Mathematica give me the solution of a problem it has solved in terms of functions that I have predefined? The specific problem I'm trying to solve is: ...
1
vote
3answers
307 views

TrueQ - Test of inequality [duplicate]

I want to look if a term is <0,>0 or ==0. What is wrong when I write ...
3
votes
2answers
604 views

FindFit for a differential equation model with multiple variables?

I'm trying to figure out how to use FindFit with a multivariable differential equation model and data. I've successfully made it work for the one-variable version ...
1
vote
2answers
295 views

Approximate solution to system of polynomial equations

I'd like to solve approximately the following system of equations for $a_1$, $a_2$, $\alpha_1$ and $\alpha_2$ all real and nonzero: ...
0
votes
1answer
70 views

LMS distance from a point to an InterpolatingFunction

I have a short script to NDSolve a second-order nonlinear BVP, which as its output produces an InterpolatingFunction object. I ...
0
votes
0answers
168 views

System of integral equations with integrals on both sides

I'd like to solve the following equation numerically for $a_1$, $a_2$, $\alpha_1$ and $\alpha_2$: $\displaystyle\int_0^{\infty}\Big[L_1\Big(\frac{k^2}{2}\Big)\Big]^2e^{-k^2}L_m(k^2)\ dk=$ ...
5
votes
1answer
184 views

Verify Harmonic Addition Theorem with Mathematica

I've calculated the harmonic addition theorem and would just like to check my result with Mathematica. However, ...
3
votes
1answer
246 views

Minimizing a potential using Solve

I am having problems minimizing a potential: $\text{V}(h,\eta)=\gamma \left(-h^2\right) \left(\eta ^2 \cos ^2(\theta )+\eta \cos (\delta ) \sqrt{-\eta ^2-h^2+1} \sin (2 \theta )+\left(-\eta ...
0
votes
0answers
114 views
0
votes
1answer
167 views

Solve doesn't return all solutions [duplicate]

I got a simple cubic equation as input, but Mathematica does not give all solutions, why is this the case here? ...
49
votes
2answers
5k views

What is the difference between Reduce and Solve?

Solve and Reduce both can be used for solving equations. Just by working with them, I know there are some differences between ...
1
vote
1answer
153 views

Minimum value with two factors

Approximate the minimum value of $2e^{x-2}-6x+xe^{x-2}$. Is my input correct? If not can you please correct it? ...
8
votes
3answers
2k views

First positive root

Simple question but problem with NSolve. I need help how to extract first positive root? For example: ...
8
votes
1answer
197 views

Unexpected behaviour of Solve applied to two equations in two variables

I have a simple Mathematica expression Solve[{a(a-1)Sqrt[1+a^2+b^2] == b(a^3-1), b(b-1)Sqrt[1+a^2+b^2] == a(b^3-1)}] which returns (on version 8.0, and also ...
0
votes
1answer
933 views

Equation with complex numbers and 2 variables

I have an equation: eq = 1 + ( 9 / ( s*(s + 9) ) )*( k/(s + b) ) == 0; where s == -2 + 2I (...
3
votes
1answer
2k views

NSolve: Mathematica 9 issue

In Mathematica 8 the following expression evaluates and returns a result in terms of InverseFunction: ...
0
votes
0answers
248 views

Solving stochastic master equation

Can someone help please me in solving the following stochastic master equation for the density matrix $\rho$? where $\rho$ is the density matrix, $\sigma_i$ are the pauli matrices, $dt$ is the ...
5
votes
2answers
335 views

How to find monotonically increasing intervals of a function

I tried this code, but not working Clear[f]; f[x_] := x^3 - 3 x + 2; ForAll[{x1, x2}, x1 < x2, f[x1] < f[x2]] Reduce[%, {x1, x2}, Reals] I expected the ...
2
votes
2answers
401 views

Count and plot the number of solutions in an interval

I have equations depending on one or more parameters and I want to find and plot regions in the parameter space in which there is a specific number of solutions. For definiteness let's consider a ...
0
votes
0answers
252 views

Defining extra boundary conditions for NDSolve?

I have a second order reaction / diffusion type ODE of the form $\frac{D_{o}}{r^2} \frac{d}{dr}\left(r^2 \frac{dC}{dr} \right) - \frac{aC}{C+k} = 0$ where $a, k$ and $D_{o}$ are constants and $C$ is ...
2
votes
2answers
662 views

Quadratic programming problem

I am trying to solve a (Sequence) Quadratic Programming (SQP) problem in Mathematica. Here’s the problem setup: ...
1
vote
2answers
318 views

How to pick a solution from a list of solutions using a test?

I have a list of solutions that depends on a parameter b3 and I'd like to get the solution for which the x value is minimal when ...
0
votes
0answers
182 views

symbolic solution for a system of nonlinear equations in mathematica

Would appreciate any help on the following in mathematica I cant figure it out. I have a system of equations that I am trying to solve symbolically. I have 9 equations and 8 unknowns (I have also ...
0
votes
1answer
128 views

InputField equations and Solve

I'm trying to get this piece of code to work: ...
0
votes
1answer
569 views

How to find the zero of a function?

I want to find out when a function has a real root. I first made a RegionPlot3D when the function is zero. ...
7
votes
2answers
477 views

Is there any fast way to solve a quadratic matrix equation in Mathematica approximately?

Let the square nonsingular matrix $M$ is a given convergent matrix. What are the best scalar values for $\alpha$ and $\beta$ (in the real numbers domain), at which the following quadratic matrix ...
0
votes
3answers
220 views

Given a Boolean representation of a system, how can the Reliability Function be displayed as symbolic algebra?

Can Mathematica 9 convert a Boolean representation of an RBD to its symbolic algebraic form? If I have a simple series Reliability Block Diagram made up of 2 components, c1 and c2 bexpr1=And[c1,c2] ...
7
votes
2answers
728 views

Alternate parameterization of a line

There are several ways to specify a line. In Mathematica's graphics, it is done by specifying two points and then connecting the points with the Line command. But ...
0
votes
1answer
62 views

Errors in evalauting an expression

I have the following: Constants: b3b = 2; G = (1/eps^2); a1 = 3; a3 = 4; xc = 0.3; Functions: ...
0
votes
2answers
203 views

Solving Within InverseCDF

I have the following input data: Remove["Global`*"] x = 5/30 // N; y = 0.8; μ = 0.2; T = 5; ρ = 0.8; σ (*to be determined*) And this is the given equation: ...
0
votes
0answers
413 views

Using Solve Within Manipulate to Model Feedback Control System Problem

This post is extremely long and I do apologize - but please bear with me with all the explanation of the context of the question - due to how long the code is I have included a hyperlink where you can ...
3
votes
1answer
265 views

ParametricNDSolve and Constraint satisfaction problem

I am trying to find the values of two parameters that allow for a specific result of my differential equations, under different initial conditions. Given a system of equations: ...
1
vote
1answer
452 views
1
vote
2answers
310 views

Error using Solve on Matrix Multiplication

I am trying to make a function the will find that value of $x$ in the following equation: $x.a=b$ all values of $x, a, b$ are matrices. The dimensions of $x$ are unknown, but $a$ and $b$ have the ...
0
votes
0answers
64 views

Defining functions in a loop [duplicate]

I have a symbolic solution to a linear system with respect to some variables a[i,j] which depend on a parameter t. sol=Solve[...,Table[a[i,j],{i,0,n},{j,0,n}]] I ...
6
votes
2answers
494 views

Very long Refine/Solve batch run - is my code broken, or just complicated?

So I'm trying to run some Mathematica code in batch mode from my university cluster. Specifically, I'm trying to find the equilibria of a system of ordinary differential equations. Inspired by the ...