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

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9
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1answer
668 views

Complex valued 2+1D nonlinear PDE using NDSolve

I am trying to follow the main ideas presented in this question, applying it to my own problem, which is a complex, time-dependent, nonlinear PDE: $$i \frac{\partial \psi}{\partial t} = \left[ ...
9
votes
2answers
1k views

RootSearch for complex or multiple equations

First the background. I'm trying to solve for the roots of a rather messy complex equation. This is not the exact equation, but it's a decent (simpler) stand in: ...
8
votes
3answers
3k views

First positive root

Simple question but problem with NSolve. I need help how to extract first positive root? For example: ...
8
votes
4answers
577 views

Defining a Unique Domain for Solving Diophantine Equations

I am working on a research problem in discrete geometry to do with sphere packings, and believe it or not, I have been able to reduce it to finding the solutions to the Diophantine equation, $$n = ...
8
votes
2answers
742 views

How do I solve this equation?

I want to solve the equation $$ f(f(-1)) = \sqrt{2} + g(f(2)), $$ where $$f(x) = \dfrac{a}{x^2} - 3x + 2, \quad g(x) = a\cdot \sin 2x$$ $a$ is unknown. The solution is $a \approx{-5.81}$. I tried ...
8
votes
3answers
1k views

Checking if the roots of a function are real

I'm trying to determine if the roots of a function are real. How would you do that? (In particular I'm interested in verifying that the roots of LegendreP[6, x] ...
8
votes
2answers
237 views

How can I get the solutions of $x^n-x-t=0$ in hypergeometric form?

$x^3-x-t=0$ has three roots that can be expressed in hypergeometric form, for example $$x_1=-1-\frac{t}{2}{_2F_1\left(\frac{1}{3},\frac{2}{3};\frac{3}{2};\frac{27t^2}{4} \right)}+\frac{3t^2}{8} ...
8
votes
2answers
2k views

NDSolve with vectors

I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ...
8
votes
3answers
717 views

How do I make Reduce yield all solutions explicitly?

Say I want to do the following: Reduce[ x+y+z==1, {x,y,z}, Modulus -> 7 ] then I get a solution with parameters, C[1] : ...
8
votes
1answer
1k views

Handling failed FindRoot calls

I want to handle FindRoot calls which did not converge (e.g "thrown" error message FindRoot::cvmit) ...
8
votes
3answers
348 views

Is there a relatively quick way to solve my integer-valued equation?

This is a very simple problem. It can be solved by nested Forloops that exhaustively test every possible case, throwing out all non-solutions. Find all the ...
8
votes
2answers
494 views

Finding all points of period n in an iterated map

I'm trying to implement an algorithm of Jenkinson and Pollicott to calculate the Hausdorff dimension of a Julia set for the map $f_c : z\mapsto z^2 + c$. It's described on page 40 of their paper, ...
8
votes
4answers
233 views

Combining solutions while solving

Here is a simple representation of my problem. I want to solve Solve[(w^2*c^2 /. #) - 1 == 0, w]& /@ {{c -> 1}, {c -> 2}} ...
8
votes
2answers
994 views

Alternate parameterization of a line

There are several ways to specify a line. In Mathematica's graphics, it is done by specifying two points and then connecting the points with the Line command. But ...
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
901 views

Number of iterations in NSolve

In Excel's solver, one can define how many iterations are to be done, to one's liking. I am wondering if this is possible to do with NSolve in Mathematica? Code ...
8
votes
3answers
857 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 ...
8
votes
2answers
1k views

How to find the maximum value of an integer that satisfies some inequality

Consider the following Mathematica expression: Reduce[2^j/(j + 1) <= 10, j, Integers] which outputs: ...
8
votes
2answers
251 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...
8
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3answers
972 views

Can Mathematica solve this sort of functional/differential equation?

I am looking for differentiable functions $f$ from the unit interval to itself that satisfy the following equation $\forall\:p \in \left( 0,1 \right)$: $$1-p-f(f(p))-f(p)f'(f(p))=0$$ Is there a way ...
8
votes
2answers
130 views

Numerical solve question

Why does this work? Solve[5 Tan[t] + 9 == 0 && 0 <= t < 2 Pi , t] {{t -> π - ArcTan[9/5]}, {t -> 2 π - ArcTan[9/5]}} But this doesn't. ...
8
votes
1answer
251 views

FindRoot kills kernel

Bug introduced in 7.0 or earlier and fixed in 10.1.0. I'm having problems with FindRoot killing the kernel. In my real application, I want to ...
8
votes
1answer
446 views

Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
8
votes
1answer
268 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 ...
8
votes
1answer
202 views

Unexpected behaviour of Solve applied to two equations in two variables

I have a simple Mathematica expression Solve[{a(a-1)Sqrt[1+a^2+b^2] == b(a^3-1), b(b-1)Sqrt[1+a^2+b^2] == a(b^3-1)}] which returns (on version 8.0, and also ...
7
votes
3answers
2k views

Finding the number of solutions to a diophantine equation

I want to count total number of the natural solutions (different from 0) of the equation $2x + 3y + z = 100$, but don't know how. How can I calculate it using Mathematica? I tried: ...
7
votes
4answers
791 views

Solving $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}+\frac{3 W}{2}$ for $W$

When I solve the aforementioned equation for $W$ or $A$ on Mathematica I get a long and ugly equation in return, namely one of the solutions for $W$ is: (attempt to read at your own health) ...
7
votes
6answers
762 views

Finding where two parametric paths cross?

I have been looking through other parametric equations questions and am still unsure where to start with this one. I am given two functions: ...
7
votes
3answers
567 views

Efficient code for solve this equation

We have $a*b*c=-1$, $\frac{a^2}{c}+\frac{b}{c^2}=1$, $a^2 b+a c^2+b^2 c=t$ What's the value of $a^5 c+a b^5+b c^5$? I tried ...
7
votes
4answers
474 views

How to find a tangent line with 2 points of tangency for a curve?

Say I have a function like this: f[x_] := 4 x^4 - 9 x^3 - x^2 + 10; Plot[f[x], {x, -1, 2}] It's obvious that there's a tangent line with 2 points of tangency ...
7
votes
5answers
481 views

Why is FindInstance finding non-instances?

Consider this example: FindInstance[Exists[{x, y}, x > 1 && y > 1 && x > Sqrt[x + y]], {x, y}] which finds values of $x$ and $y$ such ...
7
votes
3answers
207 views

Find the number of $n$ such that $n!$ is a sum of three squares

I want to check the following theorem by using Mathematica: $\textbf{Theorem} $. $\text{The estimate}$ $\# \{n \le x:n! \text{ is a sum of three squares}\}=7x/8+O(x^{2/3})$ ...
7
votes
4answers
436 views

How to eliminate variables when using Solve[]

In certain problems, we need to solve systems of equations and get results in terms of just selected variables. For example, how could we solve eqn==0 below for ...
7
votes
4answers
481 views

Manipulating Equations

I would like to be able to manipulate algebraic equations. For example, let's say I enter 3x+5==2 I would next like to be able to manually subtract $2$ from both ...
7
votes
3answers
3k views

How to solve an overdetermined system in Mathematica

I would like to understand the reasons and find a way to avoid such behaviour of the Solve function in Mathematica 8. ...
7
votes
2answers
394 views

How to read complicated result from Reduce?

How can I read this Reduce output from Mathematica that I got from solving an inequality? I do not perfectly know when one case in this case analysis is over and ...
7
votes
3answers
373 views

Can't figure out how to plot this function

I've got a real nasty function that I can't figure out how to plot. The function is $\qquad f(k) = \pm\sqrt{1+4\cos^{2}(k/2)+4\cos(k/2)\cos(p)}$ from $k=-\pi$ to $k=\pi$, which doesn't look so ...
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 ...
7
votes
2answers
326 views

How can I find solutions for this equation?

I have a function cxyz[s1, e1, s2, e2], and I want to find at least one set of {s1, e1, s2, e2} for which the function's output ...
7
votes
1answer
3k 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 ...
7
votes
2answers
159 views

Unexpected warning from DSolve

I'm trying to solve this differential equation with respect to $x$ $$ \frac{d^2y}{dx^2}-\bigg(\frac{dy}{dx}\bigg)^2-\frac{1}{x}\frac{dy}{dx}=\frac{1}{x^2} $$ With boundary condition $y(1)=2, ...
7
votes
2answers
231 views

How to correct this, `f[a_] := FindRoot[eq == 0, {x, 0.5}]`, where `eq` contains a parameter $a$, without using `eq[a]`?

I want to solve an equation with a parameter $a$, and define the result as a function of $a$. It is something like this: ...
7
votes
1answer
741 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 ...
7
votes
1answer
1k views

How to find the smallest root

I have a continuous, differentiable, monotonic, bounded function called F[t]. If t -> Infinity then ...
7
votes
2answers
228 views

How to locate the position of a periodic orbit

These are the equations of the dynamical system ...
7
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2answers
220 views

Why does Solve and Sum give different answers when according to Table it is the same sequence?

I have been thinking about a piece of code today, but I don't understand why I get different outputs from two in my mind similar Mathematical sums. First I observe that the Table command for this: ...
7
votes
1answer
323 views

Why does Mathematica not give simple solutions to simple system of equations with powers

I trt to get Mathematica getting me the simple solutions for x and y from this system of two power equations: $$\text{Eq. 1: } z=x^{m}y^{n}$$ $$\text{Eq. 2: }z=\tau x^{m-1}y^{1-n},$$ The simple ...
7
votes
3answers
568 views

NDSolve and {C, K, Slot} and other built-ins as a variable name

The following problem is an exploration of what causes the error "Input is not an ordinary differential equation" in Mathematica as it seems to have changed from version 8 to version 9. Specifically ...
7
votes
1answer
805 views

Issue with NSolve

I defined the following function: sw[ θ_, ϕ_, h_] = 1/2 Sin[2 (ϕ - θ)] + h Sin[ϕ] Based upon whether I use Solve or NSolve, ...
7
votes
1answer
901 views

How to Simplify equations over a Ring with Mathematica?

For example, when we work over a ring, the equation x^3=0 does not imply x^2=0 or x=0, but ...