Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
31
votes
7answers
884 views
Updating Wagon's FindAllCrossings2D[] function
Stan Wagon's Mathematica in Action (second edition; I haven't read the third edition and I'm hoping to eventually see it), demonstrates a nifty function called ...
4
votes
2answers
617 views
How do I work with Root objects?
I want to solve the trigonometric equation :
$$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$
I tried
Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x]
It returns the ...
8
votes
3answers
2k views
Assign the results from a Solve to variable(s)
I understand Mathematica can't assign the results of a Solve to the unknowns because there may be more than 1 solution. How can I assign the 4 values of following result to variables?
16
votes
2answers
2k views
Can Reduce *really* not solve for x here?
Sometimes I get the feeling I'm just flailing blindly with Mathematica. Is solving for $x$ in the equation
$$ \frac{\cosh (x/2)}{x} = \sqrt{2} $$
really beyond the scope of Mathematica? I try to ...
10
votes
6answers
2k views
About multi-root search in Mathematica for transcendental equations
I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range?
Perhaps ...
7
votes
3answers
849 views
Finding unit tangent, normal, and binormal vectors for a given r(t)
For my Calc III class, I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2$, and $-1$, given $r(t)=\{t,t^2,t^3\}$.
I've got Mathematica, but I've never used it before and I'm not sure how to coerce ...
5
votes
2answers
270 views
Solve an equation in $\mathbb{R}^+$
How can I solve this equation (both numerically and literally) only in the positive reals $\mathbb{R}^+$?
Solve[x == (v0 - (A CD t v0^2 ρ)/(4m)) Cos[θ] t, t]
And ...
4
votes
2answers
581 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 ...
2
votes
3answers
257 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:
...
30
votes
2answers
716 views
What is the difference between Reduce and Solve?
Solve and Reduce both can be used for solving equations.
Just by operating them, I know there is little difference between them.
But, the only thing I know is that there is little difference, and I ...
7
votes
3answers
441 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] ...
11
votes
2answers
366 views
NSolve gives additional solutions that don't satisfy the equations!
I am trying to solve the following polynomial equations in Mathematica:
...
4
votes
1answer
360 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 ...
7
votes
2answers
323 views
Solving/Reducing equations in $\mathbb{Z}/p\mathbb{Z}$
I was trying to find all the numbers $n$ for which $2^n=n\mod 10^k$ using Mathematica.
My first try:
Reduce[2^n == n, n, Modulus -> 100]
However, I receive ...
7
votes
3answers
531 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:
...
5
votes
4answers
514 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 ...
8
votes
1answer
372 views
How do I find all the solutions of three simultaneous equations within a given box?
Sometimes, one needs to find all the solutions of three simultaneous nonlinear equations in three unknowns
$$\begin{align*}f(x,y,z)&=0\\g(x,y,z)&=0\\h(x,y,z)&=0\end{align*}$$
within a ...
4
votes
1answer
534 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 , $m_{i,j}$ ...
3
votes
1answer
472 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 ...
5
votes
2answers
408 views
Can mathematica solve this equation?
I have the following Mathematica code to solve an equation comes from isoparameteric finite element for quadratic tetrahedron element. I need to get the iteroplation fast and accurate. I only find ...
3
votes
1answer
245 views
Eliminating functions from system of PDE in Mathematica
Mathematica users,
Let's see an example of three PDEs:
How can I eliminate variables q1[x,y,z] and q2[x,y,z] from a system of ...
3
votes
2answers
1k 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) :
...
2
votes
1answer
326 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\, ...
1
vote
1answer
230 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 ...
10
votes
3answers
220 views
FindInstance with a Diophantine equation seems to go on forever
I tried to find a non-trivial integer solution to the equation
$$2012^2=a^2+b^2+c^2+d^2+e^2$$
with Mathematica but the computation takes minutes; I might be doing something wrong.
...
7
votes
4answers
435 views
Finding the roots of Hypergeometric1F1[]
I am trying to find the roots, λ, for this equation:
Hypergeometric1F1[1/4 (2 - λ /β), n + 1, β]
for certain ...
4
votes
3answers
781 views
Backsubstituting solution into FindRoot
I am trying to solve a system of equations which is dependent to an parameter alpha. So I iterate over alpha via a ...
3
votes
3answers
1k views
How to get rid of warnings when using Solve on an equation with inexact coefficients?
When I solve this equation in Mathematica 8, I can get the right answer, but with some uncomfortable warnings.
Equation:
...
0
votes
0answers
182 views
Vertices of the region defined by inequalities
I have a set of 8 inequalities in two variables $X$ and $Y$. In Mathematica, using the command Reduce I find the solution. The solution plotted with ...
18
votes
2answers
2k views
Marking points of intersection between two curves
I'm trying to illustrate the solutions numerically and graphically for an equation such as Tan[x] == x. I think I did everything ok except I wanted to mark each ...
8
votes
5answers
323 views
Create filling between two trig functions
Working with trig functions, period, amplitude, etc.
I found a worksheet at a calculus website, with some nice questions related to interpreting trig functions, at least, they provide some "fun" ...
7
votes
2answers
473 views
How to invert an integral equation
There have been numerous times when I've needed to invert an integral equation, i.e. I have something like
$$f(x) = g_1(x)\int_{0}^x g_2(x') dx'$$
for arbitrary functions $g_1$ and $g_2$, and ...
12
votes
2answers
448 views
Suppressing negative roots in Mathematica
Problem
Using Mathematica's Solve operator can sometimes lead to an output involving a positive and negative root (say when solving for a variable such as ...
11
votes
4answers
354 views
How to make a Line[] with no end?
I'm trying to do this:
In this graph, the secant points are aproximated in order to become the tangent, it seems I need some kind of function which plots a line based on two points and it's points ...
11
votes
2answers
442 views
Google Code Jam: Mountain View code review
After participating in Google Code Jam 2012 Round 2, it occurred to me that the Mountain View problem boiled down to solving a set of linear inequalities, which could be done in Mathematica. I've only ...
9
votes
2answers
3k views
Figuring when the minute and hour hand coincide on a clock
I would like to list all possible times in a 12-hour period, where the hour hand overlaps the minute hand completely. This is really a question about three distinct things - to be done in Mathematica ...
8
votes
2answers
154 views
Trouble getting FindInstance to return multiple results for certain constraints
I'm having a hard time getting FindInstance to return multiple results. Consider this simple example:
...
4
votes
2answers
209 views
All possible solutions to the Matrix Equation (free variables appearing)
I am attempting to solve a system of linear equations using LinearSolve[] . In my case, the number of unknowns are more than constraints. I learnt that LinearSolve ...
4
votes
1answer
439 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 - ...
3
votes
2answers
173 views
How can I solve an equation with symbolic coefficients?
I want to try to solve the following
a x^(17/6) - b x^2 - 1 == 0
where a and b are ...
14
votes
1answer
239 views
Strange behaviour of Reduce for Mod[x,1]
For every integer $x$ the equation Mod[x, 1] == 0 holds. While
Simplify[Mod[x, 1] == 0, Element[x,Integers]]
gives ...
14
votes
2answers
473 views
Using the Krylov method for Solve: Speeding up a SparseArray calculation
I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in MMA (which I found through this SO answer): essentially I want to differentiate noisy data. The full ...
11
votes
1answer
137 views
Solve[ ] with Method -> Reduce gives a different result than Reduce[ ]
Why does
Solve[Sqrt[x + Sqrt[x]] - Sqrt[x - Sqrt[x]] ==
m Sqrt[x/(x + Sqrt[x])], x, Reals, Method -> Reduce]
give a different result than
...
4
votes
2answers
322 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:
...
3
votes
1answer
445 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?
...
2
votes
2answers
438 views
Why doesn't Mathematica solve $x=\cos\,x$ properly?
Why doesn't Mathematica solve x == Cos[x] properly?
Both Solve and NSolve fail with the ...
8
votes
2answers
227 views
Is there a way to use functions like Prime[n] within Solve[]?
I'm trying to see if a number can be written as the sum of two prime numbers. Ideally, I would like to use
Solve[Prime[n] + Prime[m] == 100, {n, m}]
But that ...
7
votes
1answer
95 views
How to plot inequalities taking into account that points must be integers and not reals?
I have solved with Mathematica 9 the following integer inequalities using Reduce:
...
7
votes
3answers
293 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
2answers
666 views
Inverse of a complicated function
Mathematica is struggling to find the inverse of this function f(r):
...
