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

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2
votes
3answers
248 views

Minimization problem

How could you find the smallest constant $c$ that satisfies $$\frac{3^{3k}e\sqrt{3}}{\pi\sqrt{k}\;2^{3/2+2k}} \leq 2^{\;c\;k}$$ assuming $k\geq 1$ is an integer. You can of course take logs of ...
1
vote
0answers
99 views
-2
votes
1answer
270 views

Transcendental equation Non-linear how to solve [closed]

I am trying to solve the following NON linear system: ...
5
votes
1answer
167 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
214 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
93 views

Mathematica returns different results when requested by Reduce, Solve [duplicate]

When I request with Reduce, Mathematica returns: ...
2
votes
1answer
442 views

Nonlinear least squares

I have a typical nonlinear least square problem and it seems very similar to the example provided in the section on parameter fitting at the Wolfram website. Unfortunately I always get some error ...
3
votes
2answers
426 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 ...
0
votes
1answer
146 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? ...
1
vote
1answer
138 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? ...
5
votes
1answer
350 views

Issue with NSolve

I defined the following function: sw[ θ_, ϕ_, h_] = 1/2 Sin[2 (ϕ - θ)] + h Sin[ϕ] Based upon whether I use Solve or NSolve, ...
0
votes
3answers
336 views

How can I solve my system of two simultaneous equations?

How to solve the system {b - a*Sqrt[a^2 + b^2 + 1] - a^2*(a*b - Sqrt[a^2 + b^2 + 1]) == 0, a - b*Sqrt[a^2 + b^2 + 1] - b^2*(a*b - Sqrt[a^2 + b^2 + 1]) == 0} ...
19
votes
4answers
2k views

Find eigen energies of time-independent Schrödinger equation

I'm trying to get the eigenvalues of a one dimensional time-independent Schrödinger equation, $-\frac{h^2}{2m_0}\frac{d^2\psi}{dx^2}+U(x)~\psi=Ei~\psi$ where U(x) is some potential and Ei is the ...
8
votes
1answer
193 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
477 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 (...
0
votes
0answers
157 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
212 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
440 views

Quadratic programming problem

I am trying to solve a (Sequence) Quadratic Programming (SQP) problem in Mathematica. Here’s the problem setup: ...
0
votes
0answers
173 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 ...
1
vote
2answers
168 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 ...
1
vote
1answer
159 views

Dsolve too slow — is there anyway around?

I am trying to solve: ...
5
votes
1answer
914 views

Solving a system of linear equations modulo n

I have a system of linear equations $$ a+b+c \equiv 31 \pmod{54} $$ $$ 4a+2b+c \equiv 3 \pmod{54} $$ $$ 9a+3b+c \equiv 11 \pmod{54} $$ What should I input (I'm using ...
0
votes
1answer
101 views

InputField equations and Solve

I'm trying to get this piece of code to work: ...
0
votes
0answers
160 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 ...
5
votes
2answers
490 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 ...
1
vote
1answer
1k views

Solving functional equations in Mathematica

I am trying to solve functional equations in Mathematica, but got nowhere. Just a simple example: $$f(x+y)^2=f(x)^2+f(y)^2$$ for all $x,y \in R$, assuming f is a real-valued function. How should I ...
0
votes
1answer
61 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: ...
1
vote
1answer
412 views

How to integrate this cumbersome piece-wise function?

I have this systems of equation: ...
0
votes
3answers
188 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] ...
0
votes
0answers
260 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 ...
7
votes
2answers
390 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 ...
3
votes
1answer
167 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: ...
0
votes
2answers
167 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: ...
1
vote
1answer
294 views

NSolve cannot solve system of equations in Mathematica

I have the following two equations: ...
1
vote
2answers
234 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 ...
1
vote
0answers
167 views

Having Mathematica solve or help solve a set of 8 equations

There is a set of DDE's that arise in leukemia dynamics and I'd like to find the equilibrium points of the system by setting all of the derivatives equal to zero. The system can be described in ...
0
votes
1answer
414 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
1answer
194 views

Asking Mathematica to produce a function of some variables

Given $$l_0=\sqrt{\frac{\lambda_1(\lambda_0+\mu_0)}{\lambda_0(\lambda_1+\mu_1-1)}}$$ and $$l_1=\sqrt{\frac{\lambda_0(\lambda_1+\mu_1)}{\lambda_1(\lambda_0+\mu_0-1)}}$$ ...
0
votes
0answers
62 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 ...
4
votes
1answer
174 views

How to demonstrate lack of stability with advection equation

I am trying to that using a coarse grid with an explicit method for, say, the advection equation leads to an unstable solution. The trouble is Mathematica avoids unstable solutions with good ...
2
votes
1answer
114 views

Compact form for domain ranges of many variables

When one sets up an equation to solve one often needs to specify conditions on the variables such as { x>0 && y>0 && z>0 } This is not ...
3
votes
1answer
306 views

Tips for efficiently solving large system coupled (nonlinear) ODEs

I'm trying to solve a system of nonlinear, coupled ODEs, where the governing equation for the $n-th$ ODE is of the form: $\sum_k^M Q_{nk} \ddot{a}_k -\sum_{\ell}^M\sum_k^M S_n(\ell,k) \dot{a}_{\ell} ...
-2
votes
1answer
276 views

Interpolating Function inside of NDSolve

I have a problem and it seems to be connected to an Interpolating function inside of an NDSolve command. The resistivity[x] ...
0
votes
1answer
38 views

Evaluate a list of Expressions from file

I have a list of expressions in a text file. I would like mathematica to evaluate and export the results at the end of the same file or in a new file. The expressions are in seperate lines in the text ...
4
votes
1answer
553 views

Use of $Assumptions [duplicate]

I don't really understand the behaviour and the usage of $Assumption. For instance, when I set $Assumptions = λ > 0, I expect ...
0
votes
1answer
428 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. ...
1
vote
2answers
354 views

How to make a Dynamic Calculator to solve a quadratic equation?

Taking my first steps in the world of Mathematica Programming. The aim of my program was to modify Wolfram's dynamic calculator (which performs an addition subtraction and a product - in response ...
0
votes
1answer
204 views

Find root of a function defined as a Module

I have a simple module like BCdet[x_, y_] := Module[ {AuxMat}, AuxMat = Mat /. {f -> x, A -> y}; Det[AuxMat] ] where ...