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

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3
votes
1answer
59 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: ...
3
votes
1answer
698 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
79 views

Solving huge equations

I have this expression: $d=-\frac{\sqrt{\frac{780 (f+130) \left(5 d^2 (13 c+f+130)-5 d (c (f+1300)-325 (f+160))+125 \left(2 (2 c+725) f+5 f^2+104000\right)+13 d^3\right) \left(5 d^2 (52 c+17 ...
3
votes
0answers
126 views

How to get vertices of a polytope given by equalities and inequalities?

I have a polytope given by some equalities and inequalities, how can I get all the vertices of the polytope? If there's a way to deal with the one given by inequalities only, how can I reduce the ...
3
votes
0answers
282 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
100 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
134 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
769 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
342 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
3answers
232 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 ...
2
votes
2answers
112 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
4answers
260 views

find the number of integral solutions a+b+c+d+e+f = 18 [duplicate]

Find the number of integral solutions of a + b + c + d + e + f = 18 where a, b, c, d, e, f are elements of the range ...
2
votes
3answers
987 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]] ...
2
votes
2answers
815 views

Why doesn't Mathematica solve $x=\cos\,x$ properly? [duplicate]

Why doesn't Mathematica solve x == Cos[x] properly? Both Solve and NSolve fail with the ...
2
votes
2answers
162 views

Check if integer has even number of digits

I want to check if a number has an even or odd number of digits. 10 would be even because it has 2 digits 300 would be odd ...
2
votes
3answers
562 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
3answers
649 views

Finding roots of nontrivial equation

I am trying to solve the following nontrivial equation: ...
2
votes
4answers
212 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
212 views

Intersection of Osculating Circle with a Parametric Curve

I have the following Parametric plot Generated from the following: ...
2
votes
1answer
886 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
1k views

Forcing FindRoot to return only real solutions

FindRoot documentation reports that if the equation and the initial point are reals, the solutions are searched in the real domain. However, in the following case I ...
2
votes
1answer
244 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
2answers
361 views

Quadratic programming problem

I am trying to solve a (Sequence) Quadratic Programming (SQP) problem in Mathematica. Here’s the problem setup: ...
2
votes
1answer
150 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
1answer
117 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
1k 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
2answers
102 views

Puzzling behavior produced by Exists

I need to simplify a set of solutions of a system, say for example: ...
2
votes
2answers
968 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
106 views

Solving problems with the floor function

I've got the following problem: If I want to calculate the following equation, ...
2
votes
1answer
315 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 ...
2
votes
2answers
162 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. ...
2
votes
1answer
239 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
343 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
2answers
2k 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
2answers
164 views

Solve the system of equalities and inequalities

I have a system of expressions, in which each expression is an equality or inequality expression of the following form: Var = Var1 + Var2 Var $\odot$ number Var $\odot$ Var1 $\odot$ = $\leq | \geq | ...
2
votes
1answer
78 views

Possible to Solve a LocationEquivalenceTest?

I have 5 groups, each containing around 20 elements. These elements are all dependent on x. For example: Set1 = {1.5x + 1, 2x + 0.5, 1 x + 1, ...} etc. Now, I want ...
2
votes
1answer
438 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 ...
2
votes
1answer
333 views

Error/warning when using NSolve for simple equation

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

Solving a system of equations

Mathematica doesn't want to solve my exact system with 3 equations and 3 variables. ...
2
votes
2answers
97 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
361 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
2answers
354 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
323 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
451 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
142 views

How to solve this numerically?

May I ask what is the best way to evaluate ...
2
votes
2answers
184 views

Tweaking Solve for systems of polynomial equations

I am trying to solve the following system of $6$ quadratic equations in $6$ variables: ...
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? ...
2
votes
3answers
138 views

Extracting coefficients from g=a*x+b*y+c*x*y

I have a Response Surface Equation (RSE) that I'm trying to extract coefficients from. It has a form similar to: g = a*x + b*y + c*x*y; I want to be able to ...
2
votes
1answer
76 views

Solving Complex Equation Over Reals

I want to solve the equation $\frac{abi}{a+bi}=4-2i$, where $a$ and $b$ are real numbers. I know from hand-solving the answer is $a=5$, $b=-10$. How do I get Mathematica to tell me this? I tried: ...