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

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13
votes
1answer
338 views

ToNumberField won't recognize Root as an explicit algebraic number

Bug fixed in 10.0.0 In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an ...
12
votes
1answer
139 views

Strange result of Reduce and ForAll

In the question Can Mathematica tell me if a polynomial has all real roots?, quite a few of interesting answers were given. I wanted to add another one, using quantors, and observed some strange ...
9
votes
2answers
5k views

Inverse of a complicated function

Mathematica is struggling to find the inverse of this function f(r): ...
7
votes
1answer
797 views

How to substitute the following conditions into an expression?

I have an expression: $p=a\;b\; x + b^2\; y + a\;c\; z$. I want to substitute $a\;b=1$, $b^2 = 2$ and $a\;c = 4$ to obtain $p = x + 2y + 4z$. How can I tell Mathematica to do that? I dont know how to ...
6
votes
1answer
255 views
5
votes
1answer
413 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 ...
4
votes
1answer
769 views

How do I use RSolve to solve a system of recurrence relations?

I am trying to solve a system of recurrence relations as follows. ...
3
votes
1answer
2k views

NDSolve does not respond

For some sets of constants, NDSolve gives me true solutions, but when I try for example, T = 1/(2*2200), Mathematica does not respond. What can I do? The code below ...
3
votes
2answers
4k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
3
votes
1answer
806 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\, W_{...
1
vote
1answer
786 views

Using previous two solutions as a start point in FindRoot

I need to solve a sequence of equations and I want the starting point of each new FindRoot to be the solution of the earlier FindRoot, increased or decreased by a a bit in the following way: Some ...
1
vote
3answers
500 views

Solve simple trig equation

I would like to solve this equation: $$-x\sin(x)=\cos(x)$$ But Solve in Mathematica doesn't work: This system cannot be solved with the methods available to ...
1
vote
2answers
154 views

After NumberForm I cannot apply a Sine function. Why?

After NumberForm I cannot apply a Sine function. Why? This works: sol1 = x /. Solve[x^2 - 3 == 0, x] Sin[sol1] Output = $\{-Sin[\sqrt{3}],Sin[\sqrt{3}]\}$ Also ...
0
votes
1answer
506 views

How to use `FindRoot` to solve an equation containing a parameter?

I'm trying to derive some of the results of the following paper: Electrodynamics of semiconductor-coated noble metal nanoshells, JT Manassah - Physical Review A In the paper there is matrix $\mathbf ...
9
votes
2answers
204 views

NSolve finds real-valued results in version 9, but not in version 10

UPDATE Reals also was used in the code. Actually, I tried the following simple piece of code. ...
8
votes
2answers
1k views

Find the parameter values satisfying conditions for all roots of an equation

Hi I'm very new at Mathematica. My real problems concerns a much more difficult equation with many parameters, but I want to check that the method is good, so I made up a test equation. My test ...
8
votes
2answers
263 views

What are the Method options Solve command accepts?

What are the Method options Solve command accepts? Solve has the Method option, however documentation contains no methods that it accepts...
7
votes
2answers
3k 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 ...
5
votes
2answers
382 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 ...
4
votes
4answers
175 views

Implicit function theorem to higher order

Consider f[x_, y_] := Csc[0.482` y] Sin[0.963` x - 0.482` y] + 3.247` Csc[0.333` y] Sin[0.667` x - 0.333` y] + 5.049` Csc[0.119 y] Sin[0.238 x - 0.119 y] I'...
4
votes
2answers
336 views

Roots of Whittaker W function

I am interested in finding the roots $u$ of the equation $$ W_{1,\imath b}(a)=0, $$ where $W_{\kappa,\mu}(z)$ denotes the Whittaker $W$ function, $a>0$ is a fixed parameter, $\imath=\sqrt{-1}$ and $...
4
votes
1answer
2k views

Why is Solve returning an empty list?

I evaluate ...
4
votes
3answers
254 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 ...
3
votes
1answer
206 views

Strange behavior of Reduce with a cubic equation

This equation: $(\frac{-a}{x})^2=\sqrt{\frac{1}{x}}$ at $a > 0$ and $x > 0$ has a clear solution $x=a^{4/3}$, doesn't it? However, ...
3
votes
1answer
76 views

Using result of Solve in further calculations

I'm trying to make a code for Gauss-Legendre quadrature. First I find the roots of the polyinomial with roots[n_,x_]:=Solve[LegendreP[n, x] == 0] Then I need to ...
3
votes
3answers
1k views

How can I solve Tan[t] - t == F[x] for t as a function of x?

How can I solve the equation Tan[t] - t = Ax, where A is a constant for t[x]? I know that ...
3
votes
1answer
98 views

Unable to solve equation for a variable by any method

I am looking to solve for the value of r when the derivative of the expression ...
3
votes
3answers
243 views

Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
2
votes
1answer
132 views

Undershoot/Overshoot Method for this differential equation?

I have tried to solve this equation for some weeks and I am not capable. I have read in articles that it is easy with an undershoot/overshoot method, but I don't know how to do it. $y''+\frac{3}{x}y'-...
2
votes
2answers
407 views

NSolve for high degree univariate polynomials

I am trying to solve a high degree univariate polynomial using Mathematica's NSolve command. But when I plug the solutions generated by Mathematica back to the equations, the equations are massive ...
2
votes
1answer
1k views

This system cannot be solved with the methods available to solve

I know questions about this warning have been posted a thousand times over. But I really couldn't find any solution that worked in my case. It's quite simple: ...
2
votes
1answer
752 views

How to guess initial complex value for FindRoot

I have to solve a transcendental equation for a parameter, say $\beta$. Now, the $\beta$ has a range from $ik$ to $k$ where $i$ is the usual imaginary root $\sqrt{-1}$ and $k$ is a real number. ...
2
votes
2answers
319 views

Mathematica can't minimize a function

Mathematica seems not to be able to minimize this univariate function over integer arguments, $r>2, r \in \mathbb{Z}$. ...
2
votes
1answer
188 views

How to properly interpret a seemingly contradictory result in Mathematica?

I have a problem with interpreting the results of my notebook outputs. It is important that I do not err with the interpretation. Here is the full input: ...
2
votes
3answers
554 views

Points of Intersection

How to numerically find points of intersection between pair of curves (Here,a circle and a parabola) ? Finding it a bit messy as, for a point on one curve, slope of the other is involved. ...
1
vote
1answer
122 views

How to speed or help Solve[] when it is stuck?

The code below generates a system of equations that I need to Solve[] for {c[5], c[6], c[7], c[8]} in terms of {c[1], c[2], c[3], c[4]}. ...
1
vote
3answers
254 views

Find all roots of a function with parabolic cylinder functions in a range of the variable

I want to find all roots of a function involving Parabolic Cylinder Functions. In what follows, I define 2 variables $\xi1$ and $\xi2$, which in turn depend on $\omega$. My function is then defined as ...
1
vote
2answers
294 views

Is there a better way to get the eight points of intersection?

I want to get the eight points of intersection from the equations 2 Abs[x] + Abs[y] == 1 and Abs[x] + 2 Abs[y] == 1. To solve ...
1
vote
2answers
478 views

solving for one solution to a system of polynomials

I'm trying to solve a system of equations: ...
1
vote
3answers
159 views

automatic processing of numerical results in `Plot`

First I want to solve an equation $F(x,y)=0$ for $y$ by supplying a value of $x$. (suppose obtaining the analytic form of $y(x)$ is too difficult) Then I want to plot root $y$ (numerically calculated) ...
1
vote
1answer
220 views

Solving systems of equations

So I have a set of equations like 12 of them but 13 variables. However I would like to find the numerical value of the roots for the maximum value of a particular variable. I don't know how to do that ...
1
vote
1answer
127 views

Applying N to the roots found by Solve gives complex numbers when the roots are real [closed]

I have a function which is f(x) = x^3 - 5 x^2 - x + 1. When I solve for x to find the zeros ...
0
votes
6answers
268 views

Roots of a characteristic equation. Can Mathematica solve it?

I have been using Mathematica for a few years, but with basic things. Now I need to find the first 10 roots of the following equation: ...
0
votes
1answer
225 views
0
votes
1answer
160 views

How to solve this nonlinear 2 by 2 equations?

I have a equation (x^2 + q1^2 - y^2)/2*(x + q1 - y) + (1 - 2*a)*q + 2*F = 2*(1 - a)*c[q] in q(variable) with parameters q1,a,F and function c(in variable q also, and I define it outside Solve so I can ...
0
votes
2answers
114 views

Finding all complex polynomial roots in a specified range efficiently

I need to find the roots of a rational polynomial that are near i. In the following code, I try that two different ways. First, I use a constraint to only find roots in the right region. Second, I ...
-2
votes
1answer
96 views

Solve For X inside arc-cos function (with division) [closed]

Very basic but I've been stuck for more than 12 hours trying to solver this equation 20=360/(arccos(X/3200)*2) Can anyone solve X? and explain what exactly you ...
15
votes
2answers
4k views

FindRoot Domain restriction

I am solving a system of four non-linear equations in four variables using FindRoot. I have some sense of the relationship between the variables so I don't want Mathematica to do its computations in ...