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

learn more… | top users | synonyms (5)

6
votes
2answers
783 views

Solution of equation with power series (perturbation)

So I need to use Mathematica to find the solution of $y=x- \epsilon \sin(2y)$ as a power series in terms of $\epsilon$. I'd assume I'd need to create an equation $f=x-y- \epsilon \sin(2y)$, then ...
5
votes
1answer
2k views

finding poles of a function

Is there a command to find the poles of a function $f=f(z)$? example: let $$f(z) = \frac{1}{z^2-1}$$ then we know that the poles are at $z=\pm 1$ but is there a special command in mathematica to do ...
2
votes
1answer
349 views

Problem with Sinc[x] function and rounding

I seem to be having some trouble with the Sinc[x] function, and I think it's due to rounding, but I'm not sure. The code is below, with relevant constants: ...
4
votes
0answers
168 views

Solving a nasty equation

Here's an equation that I need to solve for $t_k$ $$ \theta_0 = \tan^{-1}\left(\frac{2(w_x - m)}{p - g {t_k}^2 - 2 t_k w_y}\right) - {\frac{1} {r}} \left( \left(\frac{m}{t_k}\right)^2 + \left( ...
0
votes
0answers
58 views

NMinimize and FindRoot Issues with System of Equations [duplicate]

I am trying to solve a constrained optimization problem with a system of transcendental equations and am running into issues with NMinimize. I have a system of equations (...
7
votes
3answers
672 views

How do I find the intersection of a closed 3D curve given by numerical data with a specified plane?

I have a list of 3D data points which form a closed curve. My own data can't be easily generated analytically, but the qualitative behaviour is well represented by a parametric curve families such as ...
5
votes
1answer
355 views

How to add equations' left and right sides together?

If we have two equations E1 and E2, and instead of using Solve to solve it, we simply need to manually add them up which would allow some simplification that could ...
2
votes
0answers
201 views

Problems with Simultaneous Equation Solving

Let me first explain what I am doing and then I will explain the problem that I can't figure out. I am basically trying to solve 2 equations for 2 unknowns (a1 and ...
7
votes
2answers
2k views

Finding y given x from an interpolating function

I would like to put a dot on the point of a curve that has a specific y value but I don't know the x value. A simple example of my code is ...
1
vote
1answer
173 views

Corrected: Solve[] cannot solve simple hyperbola equations?

Is Solve[] very inefficient in solving equations involving square roots? The input below attempts to find out the explicit expression of either x or y in terms of other variables {x|y, a, c}, and c ...
1
vote
1answer
114 views

Cannot Plot Output of Solve

I'm trying to plot the output of the following function t2[x_] in ...
2
votes
1answer
640 views

Distance between 3D curves

I would like to determine the distance bewteen two representations of the Lorenz Attractor. I have two 3D representations for different initial conditions and I want to calculate the distance between ...
0
votes
1answer
441 views

Searching for roots of complex function

I'm searching for roots of complex function $$ 2\imath q \ln(-2\imath k)+\imath\pi-2\imath \Im(\ln(\Gamma(1+2\imath q)))+\ln(\frac{\Gamma(1+\imath q-\imath q x/k)}{\Gamma(1-\imath q-\imath q ...
6
votes
4answers
417 views

Am I missing anything? Solving Equations

I want to know what $ a^4+b^4+c^4 $ would be when $ a+b+c=1, a^2+b^2+c^2=2, a^3+b^3+c^3=3. $ I tried ...
0
votes
2answers
184 views

Solving numerically system with Mathematica

I'm trying to solve the following system with Mathematica: ...
6
votes
3answers
348 views

How to get the correct answer when solve this equation?

I want to find the values of the parameter $m$ to the graph of the funtion $$x^4 - 2 m x^2 + m + 1$$ has three extremal points make an equilateral triangle. I tried ...
3
votes
1answer
188 views

Finding the largest integer that cannot be partitioned in a certain way

I want to use Mathematica to solve the problem: Find the maximum $k$ such that $6x+9y+20z=k$ does not have a non-negative solution. I tried FrobeniusSolve. ...
0
votes
1answer
109 views

Solving one equation, then inputting the values into another for NonlinearModelFit

Considering the equation a*x^3 + a*x^2 + x + b == 0 I'm looking to find the best value for a and ...
1
vote
1answer
247 views

Choosing min/max values of transcendental equation

With help from here, I have succeeded in plotting the equation z = -a Log[2 Cosh[(2 f[x] + x)/a]], with f[x] being defined by ...
2
votes
3answers
2k views

Solve and plot an equation that is dependent on a transcendental equation

I am trying to plot a function that uses the values of a transcendental equation as its input values: y = Tanh[(2 y + x)/2.5] z = 2.5 * Log[2*Cosh[(2 y + x)/2.5]] ...
4
votes
3answers
860 views

Inverting a Spline-Function (Bezier or BSpline)

I would like to use a Spline-Function to describe a transformation from one range of reals to another, that is I would like to have a function which maps a value $y$ on $x$ and for simplicity let us ...
0
votes
1answer
509 views

Constraining solution's sign with NSolve

I am solving some equations in 4 variables, however, there are many solutions which are basically the same but changing relative signs of each other ... i.e. {x->-1,y->1} and {x->1,y->-1}. ...
1
vote
3answers
550 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 ...
2
votes
2answers
219 views

Finding integral points on a surface

Suppose I have a dimension formula (for a Lie algebra representation) that is as follows: $$ d(a,b) = {(a+1)(b+1)(a+b+2) \over 2} $$ Now consider the surface $F(a,b,n) = 0 = d(a,b) -n$ where $n \in ...
5
votes
0answers
93 views

Faster way to perform SameQ[Reduce[…], Reduce[…]]

I'm have some expressions that I need to confirm the equality of. SameQ[Reduce[...], Reduce[...]] works like a charm for the more simple expressions, however when ...
5
votes
1answer
240 views

Solving an inequality that contains Log expressions

How can I solve the following inequality: Log[1/2 + c^2] > (1.4) (30^5) 2^(4.5) 9 (0.6) (2.8) (1 + Log[3]) (1 +Log[ Log[c + 1]]) ? I tried ...
1
vote
1answer
427 views

How to get a solution set of a nonlinear system of equations?

I'm trying to find the solution set of {x, y} variables for the following system of equations: ...
3
votes
1answer
217 views

Cannot solve system of linear equation sums?

I cannot get mathematica to solve: The problematic code: ...
5
votes
2answers
749 views

Find all the integer numbers $a$, $b$, $c$, $d$, $e$, $f$, $k$ to this equation have three integer different solutions?

How to find all integer numbers $a$, $b$, $c$, $d$, $e$, $f$, $k$ that belong to interval $[-10,10]$, so that the equation $$\sqrt[3]{a x + b} +\sqrt[3]{c x + d} + \sqrt[3]{e x + f} =k$$ has three ...
10
votes
1answer
275 views

Efficient way to solve equal sums $x_1^k+x_2^k+\dots+x_5^k=y_1^k+y_2^k+\dots+y_5^k$ with Mathematica?

I need to solve the system of equations, call it $S_1$, in the integers $$x_1x_2x_3x_4x_5 = y_1y_2y_3y_4y_5$$ $$x_1^k+x_2^k+\dots+x_5^k=y_1^k+y_2^k+\dots+y_5^k,\;\; k= 2,4,6$$ I used a very ...
3
votes
2answers
209 views

Bounds on random number

I have a Markov Chain Monte Carlo code that uses a chi squared function to fit some data. I am running into an issue now with getting unrealistic values for some of the free parameters in the code. ...
19
votes
1answer
1k views

The Orbit and Perigee of the Flamsteed comet

Historical context This year we have the 330-th anniversary of the Battle of Vienna - one of the great formative events of European history, it took place on September 12, 1683. Kara Mustafa, Grand ...
5
votes
2answers
440 views

Reducing exponential inequalities fails

I am quite stumped by this problem : Reduce[ N^(x-y) <1 && N > 0 , x, Reals] gives the expected result ...
4
votes
2answers
302 views

find where 3 inequalities are simultaneously greater than zero

I have 3 functions: f11[l], f12[l] and f13[l], and I would like to know for which values of ...
1
vote
1answer
558 views

Prandtl-Meyer function

I'm trying to solve for Mach number based on the given Prandtl-Meyer function, however I keep getting odd error. Here is my code: ...
2
votes
0answers
545 views

I can't solve this set of equations

I am having trouble solving a set of equations in mathematica. I do not get any errors, but i don't get any answers as well. I have some restrictions on my parameters and variables in the equations ...
5
votes
3answers
984 views

Solve for the intersection point of 3 surfaces

Basically, I have three 2-torus (tilted) in 3-dimensional Euclidean space. They are expressed by parametric equations: ...
2
votes
2answers
440 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 ...
1
vote
1answer
680 views

solving a cubic equation

I need to find the minimum $r$ and the maximum $k$ of the following cubic equation for which there does not exist three distinct real roots. $rx^3-rkx^2+(r+k)x-rk=0$. Is it possible to find such $r$ ...
0
votes
0answers
452 views

Solve equations real and imaginary part separately

For my system of equations, the procedure described in Solving complex equations of using Reduce works no more. How can I separate the real and imaginary part of ...
4
votes
1answer
1k views

Error/warning when using NSolve for simple equation

I am using NSolve to solve an equation, as shown here: ...
2
votes
1answer
168 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
1answer
193 views

Symbolic Simulations

I have 9 nonlinear equations and 10 unknowns. It is not possible to obtain a numeric solution but I do get a parametric solution. It is useful in my case because I want to observe how parameters (p1, ...
3
votes
0answers
593 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 ...
2
votes
0answers
137 views

Nest for large value of n

I am working on a problem to find the Feigenbaum constant. In this problem I have to get $f^{2^n}(1/2)$ with $f(x) = kx(1-x)$. I use Nest to get $f^{2^n}(1/2)$ but ...
2
votes
1answer
143 views

Solving a system of equations

Mathematica doesn't want to solve my exact system with 3 equations and 3 variables. ...
8
votes
0answers
506 views

Creating and using an explicit piecewise function in a convenient way

I have a set of data points that define a function in the form curvePts = {data1,data2,...} where ...
2
votes
1answer
335 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 ...
3
votes
2answers
252 views

Mathematica does not understand (R^3)^(1/3) is the same as R [closed]

In the output from a calculation in mathematica stands a/((R^3*c)^(1/3)), with c and a ...
2
votes
0answers
336 views

Conditional statements in intial conditions?

This is potentially a daft question, but I thought I'd ask it; I have some material free to diffuse in a boundary between rn and ro; I've been able to get it working nicely for neumann type boundary ...