Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
3
votes
2answers
445 views
Numerically Solving two dependent Transcendental Equations
I need to solve a system similar to the following (Except it is quite large. Solving this ought to do the job):
$$ \tan[2f(t)] = 1+ t^2\ $$
and
$ f(t) $ is $ k $, such that$$ \tan[2kt]-(1+k^2) = 0\ ...
3
votes
1answer
137 views
Tracking FindRoot errors in NestWhileList and Table
I'm solving many systems of two equations by varying the initial parameters. I'm running FindRoot in a NestWhileList where the ...
3
votes
1answer
214 views
wrong use of _?NumberQ?
I am having trouble with a numerical exercise. Here's a simplified version of my problem.
I define two functions to find the solution to two constrained maximization problems:
...
3
votes
1answer
217 views
pH calculations, speeding up code involving Solve
I'm trying to calculate pH values of solutions containing water and acetic acid.
The relevant equations have been defined and I now want to find a solution using Mathematica.
For a specific acid ...
3
votes
1answer
75 views
Find point at which equation stops having roots (if it exists)
I am interested in the roots of this function:
f[M_, b_] := 1 - (2 M Gamma[2, 0, (1/M + b M)/Sqrt[b]])/(1/M + b M)
for fixed values of b. In particular I want ...
3
votes
2answers
90 views
Find condition under which variables fall away
I have a somewhat lengthy expression, looking like
expr = 1 + x + b + Pi + 2*a
Is there some way of generating a relationship between ...
3
votes
1answer
246 views
Eliminating functions from system of PDE in Mathematica
Mathematica users,
Let's see an example of three PDEs:
How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
3
votes
1answer
174 views
Result of Reduce contains duplicate terms
On my system, the result of this:
f[x_] := 2 Sin[x] + Sin[x]^2;
Reduce[f'[x] == 0, x]
contains the following expression twice:
...
3
votes
1answer
452 views
Solve pair of recurrence relations
[Corrected equations and added simple example]
Can you solve a system of (loosely) coupled recurrence relations like this in Mathematica somehow?
...
3
votes
0answers
120 views
FindRoot gives a wrong solution which obviously should not be there
I got stuck on FindRoot and I didn't see any similar problem posted, so let me explain what I am trying to do and what problem I meet here.
I try to find roots of a particular function, which in the ...
3
votes
0answers
69 views
Symbolic solution to ODE, pure InverseFunction not evaluated
I'm new to Mathematica and I don't understand why in the solution of the following ODE, the #1 in the pure function is not immediately replaced by the corresponding ...
3
votes
0answers
257 views
How can I solve this complicated custom function numerically?
I have a complicated function that calculates the total value of payments from an account into which deposits are made annually. I'd like to solve the function for a growth rate numerically, but ...
3
votes
0answers
100 views
RSolve not returning known solution
I have the following recurrence relationship for which I know the solution is given by a binomial distribution:
...
3
votes
0answers
366 views
Solving a system of nonlinear equations self-consistently
I am trying to solve a set of three non-linear equations in Mathematica. I need help with them. The Mathematica code (in plain text format) is attached below. If you copy & paste the code below ...
2
votes
3answers
239 views
Symbolic derivative of $n$-term product
I want to determine the relationship that must exist between the $x_i$ and $y_i$ such that
$$
\frac{\partial}{\partial\theta} \prod_{i=1}^n \frac{f(x_i,\theta)}{f(y_i,\theta)} = 0,
$$
where
$$
...
2
votes
2answers
97 views
Solving an equation and finding a couple of results given that they are integer
My problem is to find all solutions to an equation with 2 variables between two values that define the range of my search.
e.g., $(x+y-y²)/(1-y-x²)=0$ with solutions ${x,y} \in \mathbb{Z}$.
2
votes
2answers
442 views
Why doesn't Mathematica solve $x=\cos\,x$ properly?
Why doesn't Mathematica solve x == Cos[x] properly?
Both Solve and NSolve fail with the ...
2
votes
3answers
388 views
2
votes
1answer
531 views
Mathematica Can't Evaluate This?
I am trying to find the inverse function of $\frac{\ln{x}}{x^2}$ in Mathematica. I am using the Solve[] function to find the inverse (yes, I know about ...
2
votes
1answer
141 views
How to solve this equation with integers as a solution?
I want to solve the equation $$x^y + y = y^x + x$$
with $x$, $y$ are integer numbers. I tried
Solve[x^y + y == y^x + x, {x, y}, Integers]
How to solve the ...
2
votes
3answers
262 views
Using DSolve to solve for x[t,parameter]
I'm trying to solve an ODE with two independent variables (a cannon firing from a cliff incorporating wind resistance dependent on velocity). I've tried the following for the x-component:
...
2
votes
1answer
122 views
How to modify a matrix to satisfy a special condition?
I have matrix like this:
How do I modify this matrix to make it satisfy the following condition:
For each element {i, j} in the matrix the sum of the elements of row i must be equal to the sum ...
2
votes
1answer
467 views
Solving a system of equations in two variables
I have a system of two equations in two variables $x$ and $y$.
$$\begin{align}
F_1(a,b,c,d,e)x+F_2(a,b,c,d,e)y+F_3(a,b,c,d,e)&=0\\
G_1(a,b,c,d,e)x+G_2(a,b,c,d,e)y+G_3(a,b,c,d,e)&=0
...
2
votes
1answer
89 views
A basic problem with Solve
I have this equation:
4b*Cos[2t]-4a*Sin[2t]==4Cos[2t]+8Sin[2t]
Which I would like to solve. Without using mathematica, you can pretty easily see that a = -2 and ...
2
votes
2answers
90 views
Puzzling behavior produced by Exists
I need to simplify a set of solutions of a system, say for example:
...
2
votes
1answer
99 views
Any solution to system of equations?
I need ANY combination of 8 variables which satisfy:
a+b+c+d+e+f+g+h=0
a^2+b^2+c^2+d^2+e^2+f^2+g^2+h^2=1
a*b+b*c+c*d+d*e+e*f+f*g+g*h+a*h>2/3
Ideally these ...
2
votes
1answer
228 views
How to solve simultaneous equations faster with Compile?
I have large 6x6 matrix Uwhich is a multiplication of 15 rotational matrix. All of the elements are Sin\[theta] and ...
2
votes
1answer
327 views
Solving Simultaneous Equations
I am trying to solve two equations that take the form:
$W_0 \sqrt{1+\left(\dfrac{z}{\lambda\,\pi\, W_{0}^2}\right)}=W_1\;\,\quad \ldots(1)$
$W_0\sqrt{1+\left( \dfrac{z+0.1}{\lambda\, \pi\, ...
2
votes
2answers
481 views
How to plot an inequality?
I need some help in plotting the following inequality using Mathematica:
$$\frac{1+(x/100+0.1)\times y/100}{1.15+1.15\times(x/100)\times(y/100)}\geq 1$$
assuming $x,y\in \mathbb{Q}$, the set of ...
2
votes
1answer
141 views
Solving an equation involving a determinant
I have a matrix which doesn't include numerical values. There are four variables in it. It is defined by
...
2
votes
1answer
408 views
NSolve: Mathematica 9 issue
In Mathematica 8 the following expression evaluates and returns a result in terms of InverseFunction:
...
2
votes
2answers
1k views
Root finding in Mathematica
I am new to Mathematica. I have used the WolframAlpha online calculator to find roots of equations (listed under the heading Root in the output generated in ...
2
votes
1answer
63 views
Error/warning when using NSolve for simple equation
I am using NSolve to solve an equation, as shown here:
...
2
votes
1answer
83 views
Solving a system of equations
Mathematica doesn't want to solve my exact system with 3 equations and 3 variables.
...
2
votes
2answers
62 views
How do I generate a set of n-tuples containing integral solutions to a linear equation provided certain constraints?
Let $m,k,p$ be fixed positive integers. I want to create a table of k-tuples $(x_1,x_2,\ldots,x_k)$ comprised of solutions in positive integers to the equation below:
...
2
votes
2answers
252 views
FindRoot errors
I'm trying to solve a system of two equations in two variables for some range of parameter values. I use ContourPlot to see where I should look for a solutions and ...
2
votes
1answer
157 views
How to solve this exponential inequality?
I want to solve the exponential inequality $$8^x +18^x -2\cdot 27^x>0.$$ I tried
Solve[8^x + 18^x - 2*27^x > 0, x]
and
...
2
votes
1answer
288 views
FindRoot Infinite expression 1/0 encountered error
I have 1 equation in 1 variable, which when I use Plot, looks like this:
...
2
votes
2answers
116 views
A While Loop with two different steps/iteration
I'd like to know if there is a possibility to solve an equation in a while loop with 2 different steps. I want the step to be small at the beginning and bigger after a certain value of sigma (sigma is ...
2
votes
2answers
89 views
Defining a function by pieces using list of interpolated functions in order to use `FindRoot`
I have two lists with the interpolated functions
...
2
votes
2answers
200 views
Solving set of non-linear simultaneous equations gives PolynomialGCD::lgrexp error - what next?
I'm trying to solve a set of six simultaneous non-linear equations to get a numerical answer using NSolve:
...
2
votes
1answer
108 views
How can I get the general term of this recurrence equations?
Following is the recurrence relation:
a[1] = 1;
a[n_] := a[n - a[n - 1]] + 1
Array[a, 28]
I tried to use RSolve, but it ...
2
votes
1answer
95 views
Using NSolve on an equation that involves Mean and TruncatedDistribution
What I would like to do is create a mixture distribution that has a specified mean by varying one parameter in the distribution. To do this I've written the following code;
...
2
votes
1answer
841 views
Can Mathematica help to rearrange an equation?
I have an equation which I want to rearrange so one variable is on the left side by itself.
Normally, I would do this with basic algebra and identities.
However, is it possible to use Mathematica to ...
2
votes
2answers
161 views
How to find solutions that yield of root of unity?
I have a polynomial with coefficients that are integer polynomials in another (complex) variable. For example:
1 + (1 - v^2) #1 + (-3 - v^2) #1^2 + #1^3 &
I ...
2
votes
1answer
488 views
Solve in terms of specific variables
As part of my physics homework (which I do not need the answer for, as I did it by hand, and got the correct $$\frac{m_1 g-m_2 g \sin(\theta)}{-m_1-m_2}$$ as the answer) I would have liked to have ...
2
votes
1answer
58 views
Finding the root of a nested function with small values
I have reduced an error in my program to this line of code:
FindRoot[Nest[# (1 - #) k &, 1/2, 2^4] - 1/2, {k, 3.5}]
It works for $2^1, 2^2, 2^3, 2^4,$ but ...
2
votes
2answers
200 views
How do I get the solutions of a cubic equation in trigonometric form?
I know $x^3-3 x+1=0$ has three roots that can be expressed in trigonometric form:
$\{2\sin(10^\circ),\,-2\cos(20^\circ),\,2\cos(40^\circ)\}$.
How can I get this result with Mathematica?
2
votes
1answer
115 views
What's the difference between the following two codes?
I have two codes to find the integer numbers $m$, $x$, $y$, $z$ in the system of equations.
First code
...
2
votes
2answers
197 views
