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

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6
votes
2answers
812 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 ...
6
votes
2answers
128 views

Why is ToRadicals[] not able to handle all cases? Is there a workaround?

The documentation for the function ToRadicals says: ♦ There are some cases in which expressions involving radicals can in principle be given, but ...
6
votes
2answers
128 views

NSolve erroneously gives no solution to a polynomial system

I have a polynomial system with three equations in three unknowns, the maximum degree is 26. Two equations are symmetric, i.e. eq1(x,y,z)=eq2(y,x,z). If I search ...
6
votes
4answers
503 views

FindInstance (and Solve, …) abysmally slow on a fully determined system of linear equations and inequalities: why?

I took a quick look for FindInstance and Solve-related questions but came up empty for the aspect that I am curious about. So ...
6
votes
1answer
356 views

Buggy Reduce/Resolve function?

It seems to me that this is a clear-cut case of Mathematica actually producing the wrong answer (with no warnings). I'm trying to express the fact that for any integer, there exists a factorization ...
6
votes
0answers
100 views

Using a Mathematica index as a DiscreteVariable in NDSolve when solving a coupled set of ordinary differential equations

Context Since the explanation below of the problem to be solved is lengthy, let me preamble this by saying that I have code that works to solve the problem, but I don't know whether (1) it's ...
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 ...
5
votes
3answers
1k 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: ...
5
votes
2answers
258 views

DSolve returns a “wrong” solution

This wrong solution exists from mma9 to mma10.1: ...
5
votes
2answers
396 views

Equation solving with GroebnerBasis

I have a system of quadratic equations defined below ...
5
votes
2answers
285 views

How to solve this combination equation?

I want to solve the equation $$ 2n\cdot\binom{n}{0} + 5(n-1)\binom{n}{1}+13(n-2)\binom{n}{2}+\cdots + \left(2^{n-1} + 3^{n-1}\right)\binom{n}{n-1} = 1685. $$ or using alternative notion for binomial ...
5
votes
2answers
339 views

Optimum number of cog teeth for two step helical gearbox

Note: Cross-posted at http://community.wolfram.com/groups/-/m/t/137895?p_p_auth=8QnKtT9I. I am to design a two step gearbox. The first step is to choose the number of teeth in each cog wheel in ...
5
votes
1answer
244 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 ...
5
votes
3answers
713 views

Solving a system of equations with conditions related to the number of solutions

The equation below describes a conic with oblique axis: $$9 + 22 x + 9 x^2 + 46 y + 24 x y + 16 y^2=0$$ It is a parabola, as the coefficients in $x^2$, $y^2$, $xy$ form a perfect square. To find the ...
5
votes
2answers
250 views

Solve for $a$ as a function of $\beta$?

I am trying to solve this equation: $$\beta^{-a} \Gamma(a) \sin(a \pi) + e^\beta \beta^{2 a - 1} \Gamma(1 - a) \sin(a \pi) = 0$$ I tried the following: ...
5
votes
2answers
2k views

Error (NSolve::ifun) when using NSolve, I need help interpreting the error

I wrote the following code to observe how the solutions to the equation $(e^{i a})^2 = e^{i b}$ varied as $b$ varied between 0 and $2\pi$ ...
5
votes
2answers
153 views

Reduce applied to vectors doesn't work right?

Reduce[{x,0}=={0,0}, x] gives x==0 as it should, but Reduce[{x,0}!={0,0}, x] gives False, which indicates no solution ...
5
votes
2answers
459 views

Finding Points of Tangency of a Circle and a Parametric Curve

I have the following Parametric plot Generated from the following: ...
5
votes
2answers
383 views

How to find monotonically increasing intervals of a function

I tried this code, but not working Clear[f]; f[x_] := x^3 - 3 x + 2; ForAll[{x1, x2}, x1 < x2, f[x1] < f[x2]] Reduce[%, {x1, x2}, Reals] I expected the ...
5
votes
4answers
2k views

How to solve this logarithmic equation?

The equation $$x^2\cdot\log_2\dfrac{3+x}{10}-x^2\cdot\log_{\frac{1}{2}}(2 + 3x)=x^2 - 4+2\cdot\log_{\sqrt{2}}\dfrac{3x^2+11x+6}{10}$$ has two solutions for x, namely 1 and 2. I tried ...
5
votes
2answers
246 views

When does the real part of Zeta vanish on the critical line?

This seems to be a quite a simple problem but I cannot make it work. I am trying to find all values within a given range for which the real part of the Zeta ...
5
votes
4answers
2k views

How to get exact roots of this polynomial?

The equation $$ 64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0 $$ has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
5
votes
1answer
359 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 ...
5
votes
3answers
184 views

Finding the conditions for degenerate solutions to a cubic equation

I have a cubic equation (corresponding to the band structure of a physical system) given by w in the code below. ...
5
votes
3answers
311 views

Not able to get a solution to a Lagrange Multiplier Equation

I assigned several constrained optimization problems to my calc IV students to solve with Mathematica, but this one is being stubborn. The function to optimize is: f(x,y,z) = y Exp[x-z] with the ...
5
votes
2answers
282 views

Counting Real roots

I'm interested on how to count the number of real roots of a random polynomials in an instant, how to put the result in a table and how to plot it in a graph.I generated 1 million random polynomials ...
5
votes
1answer
2k views

Solving a system of linear equations modulo n

I have a system of linear equations $$ a+b+c \equiv 31 \pmod{54} $$ $$ 4a+2b+c \equiv 3 \pmod{54} $$ $$ 9a+3b+c \equiv 11 \pmod{54} $$ What should I input (I'm using ...
5
votes
2answers
390 views

Using RSolve correctly

I am having problems persuading Mathematica to solve even the simplest recurrence relations. As an example, how would you do the following? ...
5
votes
1answer
447 views

Using external variable as a variable inside WhenEvent & NDSolve

I'm trying to use the new WhenEvent functionality of NDSolve in Mathematica 9, in order to perform an action when a variable in the system reaches a certain value. I would like this variable to come ...
5
votes
2answers
2k views

Select Solution with real (positive, etc) coefficients - ignoring variables

I often need to solve equations for numerical coefficients while preserving numerous variables (e.g. to preserve scaling relations). Thus I end up with a set of solutions like $$ ...
5
votes
1answer
1k views

How Can I use Solve/Reduce Output

Suppose I want x and y to be rationals Solve[ x^2 + y^2 == 1, {x, y}, Rationals] I am ...
5
votes
2answers
2k views

Solving a trig equation

I am trying to find an explicit solution to a trigonometric equation. It is running for a long time and I didn't get any result, but Maple solves it quickly. Why ? ...
5
votes
1answer
178 views

Solution to $y = x^x (1-x)^{(1-x)}$ for $x$ [closed]

Does anyone have any insight to a symbolic Mathematica solution to this equation for $x$ in terms of y? Symbolic of any sort, just not numeric. $$y = x^x (1-x)^{(1-x)}$$
5
votes
2answers
107 views

Initial time as parameter in ParametricNDSolve

I need a help with the function ParametricNDSolve. My goal is solve the equation \begin{array} &&\dot{x}(t) = y(t) \\ &\dot{y}(t) = x(t)-1-\varepsilon Cos(\omega t) \\ &x(t_0) = x_0\\ ...
5
votes
3answers
423 views

Equation is solved quickly using Solve but takes too long using NSolve

I have the following simple command to solve for h in an equation: Solve[(1 - 2.25577*^-5*h)^5.25588 == 0.9644952131579817, h] ...
5
votes
2answers
286 views

How to get $x$ in terms of $y$ and $w$ from $w = a p x^{p-1} \left(a x^p+b y^p\right)^{\frac{1}{p}-1}$

I'm having trouble to solve the following equation for $x$ both manually and in Mathematica: $\quad \quad w = a p x^{p-1} \left(a x^p+b y^p\right)^{\frac{1}{p}-1}$ In Mathematica notation: ...
5
votes
2answers
310 views

Why doesn't Roots work on a certain quartic polynomial equation?

In everything that follows I am using Roots to get the solutions to the equations. I start off with this equation: $$ \frac{A}{3}x^4 - x^2 + 2ax - b^2 = 0$$ Now ...
5
votes
2answers
427 views

Intersection of two splines

I have a collection of sets of points, each set defining the segment of a (nice) curve on the unit sphere $S^2 \subset \mathbb{R}^3$. The points are computed numerically. I now want to compute the ...
5
votes
2answers
156 views

Solve for x given an interpolation function, y

Given a list of data, lst={{x1,y2},{x2,y2},...,{xn,yn}} and the interpolation function fun, y=Interpolation[lst] which ...
5
votes
1answer
291 views

Solving a nonlinear, second order d.e. in Mathematica

I am trying to solve the following differential equation $$ s''(x) = \frac{8}{9}s(x) -2s^2(x) + s^3(x), $$ with boundary conditions $s(-30) = 4/3 $ and $s(30)=0$, in Mathematica by using the following ...
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 ...
5
votes
1answer
105 views

Closed form of two-layer recurrence

I am trying to find a closed-form expression for $A(0)$, described by the following recurrence forms, as a function of $L$ and $d$: \begin{align} A(\ell) &= 1 + 2^d A(\ell+1) + \sum_{g=0}^{d-1} ...
5
votes
2answers
520 views

Find all roots in range

Is there any way to check for all roots in a range? Jens' findAllRoots function is pretty good, but runs at approx. 10% of roots missed when I ran a quick check on ...
5
votes
1answer
131 views

NDSolve solution violates initial conditions

I have the following code: ...
5
votes
2answers
225 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 ...
5
votes
2answers
404 views

Adding noise to nonlinear control system using NDSolve

I have a nonlinear control system ...
5
votes
2answers
287 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 $a,b,\mu,\nu$ ...
5
votes
1answer
4k 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 ...
5
votes
2answers
122 views

How to find an estimated root efficiently with binary stochastic estimation of the function?

I am trying to construct certain nice geometric patterns, and one particular feature I'm trying to optimize is the balance of black and white corresponding to point being inside, or outside a ...
5
votes
2answers
256 views