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

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0
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1answer
149 views

Reduce Cannot Solve Complicated Function

As per the answer to this question: SolveAlways rejects inequality, I tried the following commands: ...
0
votes
0answers
53 views

Finding a certain invariant polynomial using matrix coordinates

Here's a math problem that I would like to solve. This is also my first time posting on the Mathematica stackexchange website so please excuse me if this looks messy. Let ...
0
votes
2answers
56 views

Help needed with Simple equations [closed]

take a simple formula like Ohm's law u=i*r... is it possible to solve for i without values??, something like Solve[u=i*r, i] and expect an output like i=u/r which gives me: Solve::naqs: i r is not ...
1
vote
3answers
157 views

Solve for variable in integral limit when using NIntegrate

I am trying to solve for a variable which appears in the limits of an integral, rather like in the following; ...
2
votes
1answer
95 views

NDSolve with different function lengths over time

I'm working on a cops & robbers game, and there is one single event that is very very important, the event of catching someone. I'm trying to do when any robber is catched, delete it from the ...
3
votes
2answers
145 views
1
vote
1answer
937 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
118 views

how to find root near special root [on hold]

I want to find the second root of this function ...
1
vote
0answers
198 views

Why is a bump function making NDSolve take forever to solve?

I am attempting to solve a system of relatively complicated elliptic PDEs via a relaxation technique. In particular, I am trying to solve $\textrm{div} LW = S$ where $S$ is some vector and $L$ is the ...
0
votes
0answers
44 views

DSolve cannot solve for certain branches of the solution help pls

I get an error message while trying to compute this code.. help pls ...
0
votes
1answer
40 views

How to ignore terms containing in the summation of multiplications

n=4;L=3; p0[n_Integer]:= Product[ Sum[Subscript[r, k][l, l], {l, L - 1}], {k, n}] // Expand; How to ignore terms containing three or more multiplications of [2, ...
0
votes
1answer
112 views

Symbolic matrix simplification and solving

I am trying to expand or solve an equation that contains matrices for a certain matrix, but it is not working: ...
11
votes
2answers
488 views

How can I implement the method of Lagrange multipliers to find constrained extrema?

I want to form the function $h=f-\lambda_{1}g_{1}-\lambda_{2}g_{2}$ where $f$ is the function to optimize subject to the constraints $g_{1}=0$ and $g_{2}=0$ so that I can solve the first partial ...
7
votes
2answers
96 views

Behavior of Reduce with variables as domain

When using Reduce, I accidentally put a set of variables as the domain. To my surprise, it not only seems that Reduce expects ...
-3
votes
2answers
69 views

Find the value by using FindRoot command [closed]

The equation x^4-3 x^3 = cos(3x)+3 has two real solutions on the interval from -10 to 10. Lets call these two solutions r and s. Use Mathematica's FindRoot command to find r and s. Now let M equal the ...
5
votes
1answer
218 views

Incompleteness of FindInstance

I've been playing around with Resolve and FindInstance. I know that Resolve should always ...
5
votes
2answers
156 views

How to “ReplaceAll” using a set of conditional expressions instead of a list of rules [closed]

Suppose that I have two linear functions f[x_] := f0 + f1 x g[x_] := g0 + g1 x and a (possibly rather complicated) set of conditional expressions, obtained ...
0
votes
2answers
38 views

Application on systems of equations [closed]

Lauren has 20 coins in her piggy bank, all dimes and quarters. The total amount of money is $3.05. How many of each coin does she have?
2
votes
1answer
87 views

Declaration of variables in large Linear Programming model with NMaximize

I want to solve a large LP problem using NMaximize. This is a small instance of my bigger problem: $$max \sum^{4}_{t=1}(\sum^{4}_{c=1} V_{c}*f_{c,t})\\ s.t\quad ...
3
votes
1answer
204 views

Simulating a quick return mechanism

Last time, I got a satisfying answer for simulating a toggle mechanism, just as expected. NDSolve is great. I tried playing with it (as a matter of fact, @MichaelE2 ...
3
votes
2answers
167 views

Solving Inequalities with Gamma Function

I am wondering why Mathematica outputs that the following system "cannot be solved with the methods available to Reduce". $\frac{\Gamma(\frac{1}{2}+n)}{n-1}<\frac{\Gamma(\frac{1}{2}+k)}{k-1}$ ...
1
vote
1answer
99 views

Help to solve exponential equation over positive integers

I am trying to solve the equation $\frac{4}{9} = \big( \frac{1}{3} \big) ^n + \big( \frac{1}{3} \big) ^m $ with $n$ and $m$ both positive integers. I type into Mathematica the following In:= ...
15
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 ...
0
votes
0answers
44 views

Problem with equation solving using Solve

I understand that these kinds of questions may be a bit overdone but I can't for the life of me figure out what's wrong with this piece of code. ...
4
votes
2answers
210 views

Computing the sign of the real part of eigenvalues in a 3D linearized system with 3 parameters

So I have this dynamical system given by: $$ \left\{\begin{aligned} x' &= a(y-\phi(x))\\ y' &= x-y+z\\ z' &= -by \end{aligned}\right. $$ where $\phi(x) = \mu x^3 - \nu x$ and $a,b,\mu,\nu$ ...
0
votes
0answers
79 views

Solve system of non commutative operators

I'd like to use mathematica to solve systems of linear equations, where the entries are non commutative matrices. I just tried the NC package but it doesn't help so far. For example I can solve: ...
2
votes
1answer
62 views

FindRoot: Minimum Execution Time

Is there a minimum execution time for the command FindRoot? If so, can I get rid of it? For example, if I compute the time to solve the fundtion x=0, it takes around 0.27ms per evaluation: ...
0
votes
0answers
85 views

Solving coupled transcendental equations with Nsolve

I'm trying to solve a system of coupled nonlinear equations using NSolve: ...
1
vote
1answer
152 views

Mathematica Solve Hangs Indefinitely

The following code hangs ...
0
votes
1answer
60 views

Checking result for expression

I want to verify the following result: $\sum _{y=2}^{n+1} \left(\sum _{x=y-1}^n \frac{1}{x-y}\right)=n \left(H_n^{(1)}-1\right)$ In Mathematica i try with: ...
0
votes
2answers
85 views

Simplify an expression under certain condition

I have a variable A = g / (1 + g R) Actually, if the quantity (g R) >> 1 it is possible to write A as A ≈ 1/R. How can I do this in Mathematica? I tried with Assumptions, Refine, Simplify, but i can ...
5
votes
4answers
1k views

How to find the sum all even numbers of this sequence?

I have a sequence $(u_{n})$ $$u_1= 1, \quad u_2 = 2, \quad u_3 = 3, \quad u_{n}= -u_{n-3} + 3u _{n-2} +2 u_{n-1}, \quad \forall n \geqslant 4.$$ I want to list the first $20$ terms of this sequence ...
1
vote
0answers
56 views

Gram Schmidt Process for functions [duplicate]

I want to implement the Gram Schimdt procedure to the space of functions in the following form \begin{align}‎ ‎R(y,x)=\left\{‎ ‎\begin{array}{ll}‎ f(x,y), ‎& y\leq x\\ \\‎ g(x,y), ‎& y>x‎ ...
4
votes
2answers
141 views

Is there a giant AND symbol/How to solve tons of equations simultaneously

$$\sum_{k=1}^na_k=a_1+...+a_n$$ $$\prod_{k=1}^na_k=a_1\cdot...\cdot a_n$$ $$\large{?}\small{_{k=1}^na_k=a_1~\&\&...\&\& ~a_n}$$ What in mathematica would allow me to index logical ...
2
votes
0answers
112 views

Question about Solve

I don't understand what Mathematica is doing to get these solutions. I ask it to solve two equations, the left hand side of both expressions are the same, the right hand sides differ by a ± sign. I ...
2
votes
4answers
214 views

Solving a polynomial equation with a condition of equality on roots

Let the following equation have two equal roots: f[x_] := x^3 - p x^2 + q x - r And I want to find out what the three roots are. Not knowing how to put this ...
2
votes
2answers
186 views

Tweaking Solve for systems of polynomial equations

I am trying to solve the following system of $6$ quadratic equations in $6$ variables: ...
1
vote
1answer
138 views

Methods for NSolve

I've been using NSolve a moderate (50-100 equations) size system of linear equations and it has been working splendidly (Solve ...
2
votes
1answer
324 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 ...
0
votes
2answers
130 views

Eliminate variables by dividing two equations

how is it possible to divide two equations with Mathematica? I have the following code: ...
3
votes
1answer
113 views

How to solve an equation with two variables in Mathematica

If I solved an example equation like |x|+|y|=1 numerically, I would to get a 90° rotated rectangle. If I was to plot the equation, it would result in an image like ...
3
votes
1answer
61 views

Have transformation rules to be explicitly set?

I think this problem is not the hardest one, but I can't hit on it. I want to NSolve an equation. For this equation I use a transformation rule "ampTimes". First I used it like this: ...
1
vote
1answer
162 views

Unable to solve a set of equations with Solve

I'm trying to solve the following equation using Mathematica 9.0.1.0 : ...
11
votes
6answers
1k views

How to find lattice points on a line segment?

How do I find points on the line segment joining {-4, 11} and {16, -1} whose coordinates are positive integers?
15
votes
6answers
3k views

About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...
0
votes
1answer
160 views

Solve Probability of Distribution

Why does this work: Solve[Probability[x <= t, x \[Distributed] NormalDistribution[]] == 0.95 ,t] But this doesn't: ...
0
votes
1answer
61 views

How to write a variable in terms of the other [duplicate]

I have an equation that defines a variable like y=4x+a. I had another equation, z=x+2+4, I would like to know if there is a way in Mathematica to get an expression in which z= a*y+C, in which a and C ...
0
votes
1answer
58 views

Why Solve won't work for user-defined function, used for system solving? [closed]

I have a list of x-es, that I transform into a list of tx-es. Also tao is my user-defined function that I don't know the parameters of, but I do know the values I get when I put the tx-es in it. And ...
2
votes
1answer
69 views

Simplify equation using conditions/inequalities

If I have an equation like f[x](1 + a)==0 I'd like to be able to tell Mathematica that 1+a doesn't vanish in general, and get back ...