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

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20
votes
2answers
4k 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 ...
24
votes
5answers
26k 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?
57
votes
9answers
3k 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 ...
33
votes
8answers
7k 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 ...
59
votes
2answers
8k views

What is the difference between Reduce and Solve?

Solve and Reduce both can be used for solving equations. Just by working with them, I know there are some differences between ...
18
votes
4answers
12k 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 ...
16
votes
3answers
5k views

Find all roots of an interpolating function (solution to a differential equation)

I'm trying to find all the roots of the solution to a differential equation. Using NSolve or Reduce I don't get the roots, so I'm using an iterative method which I found in physicsforums.com. This ...
20
votes
2answers
5k 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
2answers
2k views

Error entering equation in DSolve

I entered a command incorrectly as follows: DSolve[{y'[x]=y[x]},y[x],x] I am now experiencing: ...
21
votes
4answers
4k views

How to get intersection values from a parametric graph?

I have this graphed: ParametricPlot[{2.4*Cos[t] + 1.6*Cos[3 t/2], 2.4*Sin[t] - 1.6 Sin[3 t/2]}, {t, 0, 4*Pi}] It is a star, and the lines cross each other ...
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: ...
6
votes
1answer
2k 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
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: ...
6
votes
2answers
1k 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 ...
37
votes
5answers
9k views

Find eigen energies of time-independent Schrödinger equation

I'm trying to get the eigenvalues of a one dimensional time-independent Schrödinger equation, $-\frac{h^2}{2m_0}\frac{d^2\psi}{dx^2}+U(x)~\psi=Ei~\psi$ where U(x) is some potential and Ei is the ...
22
votes
6answers
6k views

Finding the intersection of a curve with an interpolation function

There are no issues trying to find the intersection points of two defined curves. ...
30
votes
2answers
12k 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 ...
14
votes
2answers
1k views

Getting an InterpolatingFunction from a ContourPlot

I have a function, say minimizeme[Ω_][β_][ϵ_] = ϵ^2 Ω - Log[2 (Cosh[2 β] + Cosh[2 β ϵ])]/(2 β); I want to find its critical points in $\epsilon$ for a given ...
15
votes
5answers
990 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 ...
1
vote
1answer
536 views

Why my differential equations become True? [duplicate]

I've been trying to solve a system of nonlinear differential equation, but the conditions are a bit weird. Two of the differentials equate to the same equation, but have different boundary ...
5
votes
2answers
284 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 ...
4
votes
3answers
2k 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: ...
20
votes
3answers
1k views

How to find numerically all roots of a function in a given range?

It is common that I search numerically for all zeros (roots) of a function in a given range. I have written two simple minded functions that perform this task, and I know of similar functions on this ...
7
votes
1answer
801 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, ...
4
votes
1answer
2k views

Error/warning when using NSolve for simple equation

I am using NSolve to solve an equation, as shown here: ...
-1
votes
3answers
3k views

How do I determine the maximum value for a polynomial, given a range of x values?

I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
14
votes
3answers
5k views

Solving a time-dependent Schrödinger equation

I want to solve the time-dependent Schrödinger equation: $$ i\partial_t \psi(t) = H(t)\psi(t)$$ for matrix, time-dependent $H(t)$ and vector $\psi$. What is an efficient way of doing this so that ...
19
votes
2answers
2k views

How do I split up a curve into chords of equal length?

I have a curve that is defined as f[x] and what I'm attempting to do is to divide the curve into equal straight lengths for a number of segments of my choosing that I've defined as nSeg. I've created ...
13
votes
5answers
1k views

Solve symbolically a transcendental trigonometric equation and plot its solutions

I currently have the equation below for a beam with a hinge at various locations, the variable a can vary between 0 and 0.5. $$ Tan\left( {a\sqrt \alpha } \right) + Tan\left\{ {\left( {1 - a} ...
4
votes
2answers
1k 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 ...
8
votes
2answers
738 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 ...
1
vote
4answers
3k views

Solve trigonometric equation

I'm looking for a solution (graphic, numeric or analytic) for a function of the form: $$a^2\tanh(x)=\tan(ax),\quad a ≥ 1,\ x > 0$$ preferably using Mathematica. Any advice?
14
votes
2answers
492 views

Behavior of Reduce with variables as domain

When using Reduce, I accidentally put a set of variables as the domain. To my surprise, it not only seems that Reduce expects ...
1
vote
2answers
975 views

Find all roots in the interval of nonlinear equation

I am struggling on how to find all the roots of 1+1/2^x+1/3^x==0 which lie in a given of real and imaginary interval. Solve ...
28
votes
3answers
1k views

Does Mathematica have a built-in tool that allows one to operate on both sides of an equation?

Geogebra has a very neat CAS view that allows one to solve an equation step by step in the following fashion: $\quad \quad \quad \quad \quad \quad \quad \quad \quad $ You type an equation and ...
9
votes
2answers
732 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 ...
13
votes
6answers
3k views

How to find lattice points on a line segment?

How do I find points on the line segment joining {-4, 11} and {16, -1} whose coordinates are positive integers?
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 ...
1
vote
2answers
860 views

Classification of a linear system of equations with a parameter

I need to get every possible value of k that returns infinite number of solutions or no solution to this system: ...
14
votes
1answer
1k 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 ...
16
votes
2answers
556 views

Determining the default Method used in optimization and root-finding algorithms

Is it possible to extract the Method which is used in functions like NMinimize, FindRoot, ...
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 ...
11
votes
5answers
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 ...
6
votes
4answers
867 views

How to find an approximate solution in a region when Solve or NSolve does not work?

Consider the relation x/Tan[Pi x] == y/Tan[Pi y] Solve or NSolve can't give a solution ...
4
votes
1answer
882 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
1answer
4k views

Finding intersection of two graphs

Here is a toy problem: I have a (directional) line that starts from {2,0} and goes through {1.8, 0.01}. Also I have a ...
21
votes
1answer
848 views

Bug in Solve (Mathematica 9)

The issue seems to be fixed as of Version 10.1. Just came across the strangest bug under both Mathematica 9.0.0 and 9.0.1. If one enters: ...
5
votes
2answers
521 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 ...
4
votes
3answers
503 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
2answers
345 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 ...