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

learn more… | top users | synonyms (4)

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
67 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
154 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
86 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
200 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
165 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:= ...
14
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
209 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
78 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
83 views

Solving coupled transcendental equations with Nsolve

I'm trying to solve a system of coupled nonlinear equations using NSolve: ...
1
vote
1answer
151 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
140 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
213 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
185 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
136 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
316 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
111 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
60 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
156 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
159 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
60 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
56 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 ...
9
votes
5answers
508 views

Create filling between two trig functions

Working with trig functions, period, amplitude, etc. I found a worksheet at a calculus website, with some nice questions related to interpreting trig functions, at least, they provide some "fun" ...
2
votes
1answer
254 views

Speeding up solving a system of simultaneous equations

I am trying to solve the following system of equations. Solve takes a very long time to solve the following system of equations. Is there any way to speed it up? ...
1
vote
2answers
163 views

Find the centre of FindGeometricTransform

I'm interested in using Solve[] to find the centre point of rotation (as an $x,y,z$ coordinate point) and axis of rotation (as a vector) from a ...
0
votes
3answers
97 views

Partial products in prime steps [duplicate]

I am trying to find out partial products going up in prime steps for Euler's product formula $$\prod_{p} \frac{1}{1-p^{-s}}$$ Trying things like ...
0
votes
3answers
130 views

Solving algebraic equations

How may I make n and k in terms of x and y in this ...
0
votes
1answer
435 views

Why does Mathematica fail to solve my equation?

I am trying to solve an equation using Mathematica, but I keep getting the following error Solve::nsmet: This system cannot be solved with the methods available to Solve. More importantly, ...
0
votes
1answer
66 views

Solving polynomial equations takes infinit time

I need to solve an polynimial equation, but when i try to use Solve or NSolve in mathematica, its cant find the solution in appropriate time (i interrupted calculation after 5 hour left). The ...
0
votes
1answer
64 views

SolveAlways rejects inequality

I have two functions of x, f and g. f[x] = g[x] + 2, ...
1
vote
3answers
172 views

Plot a table of ranges

I have table with values like: t = {1.234 <= a <= 2.345, 3.42 <= a <= 5.67, ...} and I want to plot this table, the ...
1
vote
2answers
189 views

Equating coefficients in a non-power-series equation

How can I use Mathematica to equate coefficients in a non-power-series equation? For example, I would like to take an equation like the following: ...
1
vote
3answers
297 views

How can i get the solution of complicated equation?

This is the equation about zeta. NSolve[eq] could not solve this equation. (I think it is too complex to solve by NSolve.) I ...
6
votes
2answers
1k views

NDSolve with vectors

I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...