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

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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 ...
5
votes
1answer
238 views

Incompleteness of FindInstance

I've been playing around with Resolve and FindInstance. I know that Resolve should always ...
5
votes
0answers
86 views

Using quantifiers with free indices as declarative conditions in equation solving

This is a toy example: Is there a way to rewrite ...
5
votes
0answers
1k views

Solve huge symbolic system of linear equations

I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
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 ...
4
votes
3answers
450 views

How to obtain a fixed number of solutions to $x+y=1$?

How to obtain a fixed number of solutions to $x+y=1$? For example, I want 4 solutions: $(1,0),(2,-1),(3,-2),(-2,3)$ I want to do this also on bigger equations such as $x+y+...=1$ and then I want to ...
4
votes
2answers
990 views

Can mathematica solve this equation?

I have the following Mathematica code to solve an equation coming from isoparameteric finite element for quadratic tetrahedron element. I need to get the iteroplation fast and accurate. I only find ...
4
votes
7answers
2k views

What is the equation to plot a vertical line?

Please help. Trying to find area between three curves, e^-x, x = 2, y = 1. Can't find out how to plot x = 2. Don't want to use ...
4
votes
2answers
1k views

How can I solve the equation with integers as a solution?

I want to solve the equation $$(x-1)^2 + (y-1)^2 + (z-1)^2 = 49$$ where $x$, $y$, $z$ are integer and $x \neq 1$, $y \neq 1$, $x \neq 1$. How do I tell Mathematica to do that?
4
votes
2answers
582 views

How do I solve N simultaneous equations for N variables?

I have a function: f[x_] := x + 31 x^3 + 5 x^25 Which I want to find an expansion for: ...
4
votes
3answers
474 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 $$ ...
4
votes
3answers
370 views

Finding parameters making real part of eigenvalues vanish

I have the following $\;3\times3$ matrix: $\left( \begin{array}{ccc} 0.04 -0.4 b & 0 & 0.04 -0.4 b \\ 0 & -0.08-1.2 b & -0.06-0.9 b \\ 1.04 -0.4 b & 2.08 -0.8 b & 0 ...
4
votes
3answers
1k views

How to solve this system of equations?

I want to solve the following system of equations: $$\begin{cases} 1+\sqrt{2 x+y+1}=4 (2 x+y)^2+\sqrt{6 x+3 y},\\ (x+1) \sqrt{2 x^2-x+4}+8 x^2+4 x y=4. \end{cases}$$ I tried ...
4
votes
5answers
241 views

On finding all the positive integral solutions of $x^2+y^2=z^2+1$

I am a new to Mathematica. My goal is to find many (if not all) positive integer solutions to the equation: $x^2+y^2=z^2+1$ using Mathematica. However the problem is that I can only find a ...
4
votes
2answers
639 views

How can I get the exact real solution of this equation?

I want to solve the equation Sqrt[x] + Sqrt[1 - x^2] == Sqrt[2 - 3 x - 4 x^2] with real solutions (in the real domain). I tried ...
4
votes
1answer
2k views

Solve system of equations related to perspective projection

I'm trying to solve system of equations. I have 4 points before perspective projection and after and I whant to obtain matrix of perspective projection $m_{i,j}$ ($x,y,u,v$ are known , $m_{i,j}$ ...
4
votes
2answers
749 views

How to solve for an Z-Score of a T-Distribution?

I'm looking for the Z-Score for a distribution, where the integrated area sums up to 0.90. Unfortunately I always get an error from Mathematica, ...
4
votes
5answers
497 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
4
votes
4answers
3k views

Solving complex equations

I feel like I am missing a basic, but key point when using Mathematica's Solve or Reduce. ...
4
votes
2answers
1k views

How to find regions that satisfy this inequality?

I am new to Mathematica and would like to find the set $$\{ (x,y) \in \mathbb{R}^2: (3x+y\exp(xy))(x-a) + (6y + x \exp(xy))(y-b) < 0 \}$$ for some constants $a$ and $b$. How can I do ...
4
votes
2answers
446 views

Intersection of Osculating Circle with a Parametric Curve

I have the following Parametric plot Generated from the following: ...
4
votes
2answers
357 views

Find the value of parameter so that the equation has one solution

Let $(E_l) : x^4-4x^3+x^2(5-l^2)+4 x l^2-4l^2 = 0$ be an equation with $l$ as a parameter and $x$ as an unknown and $S_l$ the set containing all the real solutions of $(E_l)$. Then there is a unique ...
4
votes
4answers
685 views

An easier way to find the properties of an ellipse from its equation?

In this Q&A about fitting an ellipse to a set of points, there are multiple answers that generated general equations of the ellipse, like this one by @ubpdqn: However, the steps to find out the ...
4
votes
3answers
476 views

How can I get the exact solution of this equation (inequality equation)?

I want to solve the equation and inequality equation $$\sqrt{8\cdot 16^x - \dfrac{1}{2}\cdot 9^x }= 3\cdot 4^x - 3^x$$ and $$\sqrt{8\cdot 16^x - \dfrac{1}{2}\cdot 9^x } \leqslant 3\cdot 4^x - 3^x.$$ ...
4
votes
3answers
859 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 ...
4
votes
1answer
563 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 ...
4
votes
3answers
867 views

Solving Integrals

Here's a problem that I don't understand. f[x_] := Exp[Cos[3*x]] g[x_] := (1/3)*x^3 - x^2 + 2 When I try to find the limit: ...
4
votes
2answers
933 views

Solving inequalities for positive Integers

Consider the following; ...
4
votes
4answers
1k views

recursively solve equation and saving the values

I am new to Mathematica. I am trying to recursively solve an equation and saving the values into a Table. Since I need the real solutions only I use ...
4
votes
1answer
415 views

How to find the integer solution number of a linear system with inequalities?

I have the following system with mixed equality and inequalities defined as: ...
4
votes
3answers
383 views

How can I find the boundary function in RegionPlot?

I have a problem with finding the function that gives the boundary curve in RegionPlot comamnd. I use the following code to make the regions in which two ...
4
votes
2answers
932 views

What is the efficient way to code Successive Over-relaxation (SOR) method in Mathematica?

I have written a SOR method (SOR is this method) code using C-style procedural loops. However, I think there might be (much) better ways to achieve the same end in Mma avoiding these loops. So my ...
4
votes
2answers
301 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 ...
4
votes
1answer
380 views

Create Euler equation

I've tried to make some research, but without any luck. How do I setup the Euler equation for this in Mathematica?: $ \text{Min} \int_0^1\left(2x^2+ \left(4t-5 e^{r \, t} \right) x \, \dot{x} + ...
4
votes
2answers
604 views

Finding all/most roots of a discontinuous function more consistently?

I have the equation: f[x_]:=α Tan[α*a] - Sqrt[c - α^2] and ideally I want to find all of its positive zeros, given a and c, with variable alpha. The problem is ...
4
votes
1answer
753 views

Reduce an equation by putting a new variable

I have the following equation given: $$ (26-x)\cdot\sqrt{5x-1} -(13x+14)\cdot\sqrt{5-2x} + 12\sqrt{(5x-1)\cdot(5-2x) }= 18x+32. $$ In order to solve it, I want to substitute $t = \sqrt{5x - ...
4
votes
3answers
1k views

Replace function and its derivatives found with Solve

If I have an equation eq = f[x] + g[x] == 0 and I solve for f[x] sol = Solve[eq,f[x]] ...
4
votes
1answer
143 views

Solving 2-D Mechanical Systems

I'm trying to use Mathematica to solve a particular 2-d mechanical system. The system comes from "DESIGN AND OPTIMIZATION OF AN EIGHT-BAR LEGGED WALKING MECHANISM IMITATING A KINETIC SCULPTURE, “WIND ...
4
votes
3answers
179 views

Regarding how to use Reduce

Say for example I am doing the following in Mathematica ...
4
votes
2answers
529 views

Why doesn't FindRoot work correctly?

I'm trying to find the roots of the following equation: I need to find λs for different values of ξ. I know that for all ...
4
votes
3answers
165 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: ...
4
votes
1answer
228 views

How to solve this trigonometric system of equations numerically?

How can the following trigonometric system of equations be solved numerically? ...
4
votes
1answer
151 views

Does `Reduce` give complete and necessary conditions?

I want to obtain a solution for a system of five inequalities. For instance, ...
4
votes
2answers
150 views

How can I get all solutions of a system of equations with Reduce?

The post What is the difference between Reduce and Solve? discusses the difference between Reduce and Solve. Now, with the ...
4
votes
2answers
189 views

Reduce with Integer domain, but receive a rational solution

I want to find the integer values $k$ so that D[f[x], x] has integer solutions. I tried ...
4
votes
3answers
215 views

Why the inequality does not take into account the domain?

I have this inequality: Reduce[(4000-1000k)/(k-4) < 0] and the answer is k ∈ Reals I would expect ...
4
votes
1answer
1k views

Error/warning when using NSolve for simple equation

I am using NSolve to solve an equation, as shown here: ...
4
votes
1answer
416 views

Find asymptotics of a function

Can Mathematica find the asymptotics of a function in the following sense? I have Log[1/n^2]/Log[4^(-Sqrt[Log[n]]) + (2^(-Sqrt[Log[n]]) - 1)^2] and I would like ...
4
votes
1answer
4k views

Why can't Mathematica “Solve” my equation?

I am trying to get Mathematica to solve the following equality in terms of $w_i$ $\displaystyle \frac{\sum_{i = 1}^{n} x_i }{\sum_{i = 1}^{n} y_i} = \frac{\sum_{i = 1}^{n} ( (\frac{x_i}{y_i}) w_i ) ...
4
votes
1answer
264 views

How to solve this Integral equation

D[x[t] - x[t - 1]/(2 E), {t, 3}] + Integrate[E^(-δ)*x[t - δ]/5^t, {δ, 2, 2.5}] == 0 I found solve this problem is hard with Mathematica. I also find a article ...