# Tagged Questions

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

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 ...
27k 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?
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 ...
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 ...
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 ...
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 ...
6k 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 ...
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 ...
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: ...
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 ...
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 ...
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: ...
10k 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 ...
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 ...
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 ...
7k 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. ...
1k 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 ...
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 ...
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. $$Tan\left( {a\sqrt \alpha } \right) + Tan\left\{ {\left( {1 - a} \right)\... 3answers 3k views ### First positive root Simple question but problem with NSolve. I need help how to extract first positive root? For example: ... 4answers 3k views ### Solve trigonometric equation I'm looking for a solution (graphic, numeric or analytic) for a function of the form:$$a^2\tanh(x)=\tan(ax),\quad a ≥ 1,\ x > 0$$preferably using Mathematica. Any advice? 1answer 814 views ### Issue with NSolve I defined the following function: sw[ θ_, ϕ_, h_] = 1/2 Sin[2 (ϕ - θ)] + h Sin[ϕ] Based upon whether I use Solve or NSolve, ... 2answers 286 views ### When does the real part of Zeta vanish on the critical line? This seems to be a quite a simple problem but I cannot make it work. I am trying to find all values within a given range for which the real part of the Zeta ... 3answers 5k views ### Solving a time-dependent Schrödinger equation I want to solve the time-dependent Schrödinger equation:$$ 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 ... 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 ... 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 ... 4answers 894 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 ... 1answer 2k views ### Error/warning when using NSolve for simple equation I am using NSolve to solve an equation, as shown here: ... 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: ... 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 ... 2answers 745 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 ... 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? 1answer 546 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 ... 2answers 1k 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 ... 3answers 4k 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. ... 2answers 576 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, <... 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 $$has seven solutions x = 1, x = -\dfrac{1}{2} and x = \cos \dfrac{2n\pi}{11}, where n runs from 1 to 5. With ... 2answers 1k views ### Can mathematica solve this equation? I have the following Mathematica code to solve an equation coming from isoparameteric finite element for quadratic tetrahedron element. I need to get the iteroplation fast and accurate. I only find ... 2answers 513 views ### Behavior of Reduce with variables as domain When using Reduce, I accidentally put a set of variables as the domain. To my surprise, it not only seems that Reduce expects ... 1answer 4k views ### Finding intersection of two graphs Here is a toy problem: I have a (directional) line that starts from {2,0} and goes through {1.8, 0.01}. Also I have a ... 3answers 513 views ### Finding parameters making real part of eigenvalues vanish I have the following \;3\times3 matrix: \left( \begin{array}{ccc} 0.04 -0.4 b & 0 & 0.04 -0.4 b \\ 0 & -0.08-1.2 b & -0.06-0.9 b \\ 1.04 -0.4 b & 2.08 -0.8 b & 0 \end{... 2answers 1k views ### How to find regions that satisfy this inequality? I am new to Mathematica and would like to find the set$$\{ (x,y) \in \mathbb{R}^2: (3x+y\exp(xy))(x-a) + (6y + x \exp(xy))(y-b) < 0 \}$$for some constants a and b. How can I do ... 1answer 427 views ### General form of a linear transformation Let v_1 = \begin{bmatrix} 2 \\ -1 \end{bmatrix} and v_2=\begin{bmatrix} 1 \\ -1 \end{bmatrix} and let A= \begin{bmatrix} 3 & 2 \\ -2 & 1 \end{bmatrix} be a matrix for T\colon \Bbb R^2\... 1answer 1k views ### How do I find all the solutions of three simultaneous equations within a given box? Sometimes, one needs to find all the solutions of three simultaneous nonlinear equations in three unknowns$$\begin{align*}f(x,y,z)&=0\\g(x,y,z)&=0\\h(x,y,z)&=0\end{align*}$$within a ... 1answer 794 views ### Nonlinear FEM Solver for Navier-Stokes equations in 2D it's me again. I'm trying to obtain a numerical solution to Navier-Stokes equations in 2D in a non-rectangular region. So far, this guide was very helpful, but he is using finite differences, which is ... 2answers 2k views ### NDSolve with vectors I'm stumped. I'm trying to write this using vectors, but the 2nd derivative isn't being expanded like I expected it to be. This is a system of equations for a projectile with quadratic drag and ... 3answers 1k views ### NSolve gives additional solutions that don't satisfy the equations! I am trying to solve the following polynomial equations in Mathematica: ... 5answers 801 views ### Create filling between two trig functions Working with trig functions, period, amplitude, etc. I found a worksheet at a calculus website, with some nice questions related to interpreting trig functions, at least, they provide some "fun" ... 3answers 293 views ### Labeling solutions of an Eigenvalue equation involving Bessel functions I'm solving the Schrödinger equation for a particle in an annular geometry with hard wall boundary conditions and I've reduced it to the following equation:$$J_m(k\,R_1)\,Y_m(k\,R_2) - J_m(k\,R_2)\,...
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 <...