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

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3
votes
3answers
131 views

Reduce gives wrong solutions

Given the follwing system of equations eqs = { x/(x - 2) - 4/y == 1, x/(2 + 1/y) == y/(3 - 1/x) } Although the domain of this system does not contain ...
-2
votes
1answer
68 views

Solving fifth order polynomial equation [closed]

I am trying to solve this equation: 1/s^3 + 3s^2 + 4s + 1 But I am not able to solve it. A little help would be appreciated. P.S: I am new to Mathematica and I ...
0
votes
1answer
82 views

Transcendental Equation

After playing around with The Planck radiation law for the spectral energy density, (differentiation and setting equal to 0 to find the maximum wavelength"x") I'm stuck on how to deal with what I'm ...
2
votes
1answer
69 views

Faster variant of Reduce for finding zeros of holomorphic functions in a region

I'm currently using Reduce to find zeros of a function in a region on a complex plane: ...
4
votes
1answer
57 views

Sequential System of Equations

I’m trying to set up this system of equations that sequential feeds into itself. I have these 2 equations I’m running. I’m new to Mathematica so I have no idea how to even start this. The basic idea ...
0
votes
1answer
55 views

Roots of a transcendental equation

I need to find the 50 first roots of a transcendental equation. I use Table and FindRoot, so I find repeated positives and negatives values in a list, but I want only the 50 first positives and ...
0
votes
0answers
79 views

First Order Conditions

I am new to Mathematica so I am not sure if this is correct. I have setup up a Lagrangian and I am trying to get the FOCs of this problem. However, it does not seem to work. Any help would be much ...
0
votes
0answers
64 views

Find first n roots of a function

Is there a straightforward way to find the first $n$ roots of a function? I have found various ways of finding roots in an interval, but none that would keep looking for roots until they find a ...
0
votes
0answers
146 views

Solve doesn't solve my transcendental equation

I want to solve a geometry problem. To do this, I need get formula for "d" in the equation: ...
1
vote
1answer
98 views

Improving Performance - Finding Polynomial Roots [duplicate]

I'm fairly new to Mathematica. In the past, my usage has mostly been limited to solving the occasional equation, making some plots, and working with small scaled statistics. None of these have been ...
0
votes
0answers
79 views

What does it mean when FindInstance returns unevaluated?

According to the documentation, FindInstance[] return the empty set when it does not find a solution and one of the examples claims that this is proof that no solution exists. So if FindInstance[] ...
0
votes
0answers
29 views

Roots of two Functions containing integrals, with two parameters [duplicate]

I want to find the values of l1 and l2 from the following two equations: ...
-2
votes
1answer
55 views

Solve on parametric equation produces inequal results

I have a parametric (parameter t) equation in two dimensions (vectors). s = Solve[pt[t] == qt[t], {a, b}] Both pt and qt are parametric lines using a and b as ...
0
votes
1answer
139 views

Time evolution of a wave packet from the time-independent Schroedinger equation [duplicate]

Starting off with the time-independent Schroedinger equation (TISE) $\quad \quad -\frac{\hbar^2}{2m} \nabla^2 \psi + V(r, \theta) \psi = E\, \psi,$ I would like to study the time evolution of an ...
0
votes
2answers
43 views

Expand “hierarchical” system of equations

I have a system for equations that is structured hierarchically: - Level 0: these are base variables that I can measure from a process (e.g. a,b,c) - Level 1: these are variables derived from Level 0 ...
1
vote
1answer
121 views

Approaches to solving non-linear systems of equation with assumptions

The specific type of system looks as follows: \begin{align} (r-r')x+4d_1 x^3+4d_{12}xy^2 &= 0 \\ (r+r')y+4d_2 y^3+4d_{12}yx^2 &= 0 \\ \end{align} Where $r,r',d_1, d_2, d_{12}$ are all real ...
0
votes
0answers
55 views

No solution for a system of equations

I am a newbie in Mathematica and I face a problem in my attempt to solve a system of equations. The system is the following: ...
1
vote
1answer
243 views

How to plot the graph of the equation F[x,y]=0 if y is real number, x is complex? [closed]

I have an equation F(x,y;a,b,c,...)=0, where x and y are variables, a,b,c,... - parameters. y is a real number, x - complex. For every given y I need to solve this equation, i.e. to find Im(x) and ...
1
vote
1answer
98 views

Solving equations bounded by a region

Straight to the point I have a function ...
0
votes
1answer
35 views

Strange behaviour of Append [closed]

I have the following situation and I completely do not understand why the second system can be solved but the first (of the same equations, as it seems) cannot. How is it possible? ...
0
votes
0answers
30 views

Problem evaluating function

Hey there I am missing the trick in evaluating following problem so that mathematica first solves the derivative of the legendre polynom and just after that it solves the whole thing for value 1 ...
0
votes
1answer
84 views

Many NSolves to interpolating function

I have an expression of the form: expr = TerribleNumericalFunction[U[p]] == SimpleFunction[p] The Simple function is a ...
0
votes
0answers
51 views

Solving Lagrangian (4 vars to solve for)

I'm a bit new to Mathematica, but here's what I've got: ...
0
votes
0answers
77 views

Solving symbolically large system of underdetrmined linear equations

I would like to find matrices 3x3, say A, B, C, such that for all symmetric matrices X, with zero trace, one has: $$AX_1+BX_2+CX_3=0, AX_2=BX_1, AX_3=CX_1, BX_3=CX_1$$ where $X_i$ denotes i-th row (or ...
0
votes
1answer
80 views

Finding gradient of equiangular (logarithmic) spiral

I encountered a problem in determining the gradient in cartesian coordinates (x,y) of a logarithmic spiral (or equi-angular spiral) profile. The log-spiral definintion is as shown below (similar to a ...
1
vote
1answer
83 views

Complicated equation solving

I want to find the maximum point or optimal value $y$ of Rx1[y_, a_, b_]. ...
2
votes
1answer
108 views

Stability Boundaries via Routh-Hurwitz Criterion

I'm attempting to determine the stability boundaries of a 2nd order system via Routh-Hurwitz stability criterion. That is to say, I need to compute when a polynomial, which is in terms of variables ...
0
votes
0answers
26 views

Some more efficient form to calculate the order value

This takes a long time, any idea how accelerate Reduce[x^(2 x^2 - 2 x) - 1 == x , x] k = x^2 + x^-2 k = ?
0
votes
2answers
66 views

Diophantine and odd

need to resolve this Diophantine equation, but with the condition that a, b, c belong to the set of odd numbers from 1-51, as I write this condition in the code ...
0
votes
2answers
93 views

Find smallest integer that satisfy a system [closed]

f[m_,n_]:=-205 m^2-(672m)n+324(n^2) I want to find the smallest positive integer M such that all of the numbers f(m,n), for m=1,2,...,M and n=1,2,...,M are ...
2
votes
1answer
118 views

Can Mathematica solve this type of recurrence?

I have the following recursively defined equation: ...
1
vote
3answers
146 views

Find value of x such that x! less than or equal to 1000

I am trying to find the maximum value of $x$ such that $x! \leq 1000$. I tried the following: NSolve[Factorial[x] - 1000 == 0, x] but I got this message: ...
0
votes
0answers
59 views

Solve[..] does not solve the equation? A bug?

I tried to get the values of CosTheta where the expression is zero and store theses in sol. ...
0
votes
1answer
58 views

Finding the intersection of two graphs [duplicate]

I'm having difficulty with finding the intersecting point of two graphs. Here is what I have done so far: Plot[{8*n^2, 64*n*Log2[n]}, {n, 0, 100}] which produces ...
1
vote
1answer
78 views

Plot roots of polynomial system of equations in 3 variables

I have the two equations $x^2 + 2y^2 + z^2 = 1$ and $xz -y^2 = 0$ I want to plot the roots in 3D. i.e the coordinates $x,y$ znd $z$
2
votes
1answer
73 views

Plotting solutions of systems in complex plane

I'm interested in plotting solutions of systems of polynomials in the complex plane, in the following way. Let $f_1,\ldots f_s$ be complex polynomials in variables $x_1,\ldots x_n$. I know how to ...
2
votes
4answers
145 views

Using ArcLength in Mathematica 10 using absolute values

With Mathematica 10, I can nicely plot: y = x^2 - 4 Abs[x] - x But I have not been able to use ArcLength to get the length of ...
1
vote
1answer
80 views

cross point of intersecting lines [duplicate]

What is the easiest way to find the crossing point of two intersecting lines passing lets say through points line1 = {p1,p2}, line2 = {p3,p4}?
1
vote
1answer
108 views

Solving ODES in order to find unknown constants

I am trying to solve a set of ODES which represent a second order consecutive chemical reaction. ...
0
votes
0answers
41 views

How to sweep a parameter in an ODEs system using ParametricNDSolveValue?

I want to analyze how my ODEs system behaves when I change only one parameter (in this case d). ...
0
votes
1answer
108 views

How to get an analytical solution for this equation set with Abs function in it?

To calculate the solution for the following equation set's unknown variables ${C,V}$ \begin{equation} \begin{aligned} \sum_{i=1}^m Abs[bt_{i} \cdot xt'_{i} - V \cdot bt'_{i}] \cdot c &== C \\ C + ...
2
votes
2answers
221 views

Solve ODE in State-space form

Is it possible to solve an ODE in state-space form in mathematica? Such as x'[t]=A.x[t] I attempted ...
-2
votes
1answer
54 views

Using functions inside Solve [closed]

I'm trying to solve a system with the function: Solve. But I am not able to use functions within the Solve, for example the ABS ...
0
votes
0answers
56 views

Reduce does not work

(i*((1 - ((1 + j)^-n))/j)) - (i*t*((1 - ((1 + j)^-n))/j))*(1/((1 + j)^k)) + (1*(1/((1 + j)^n))) == 1 I want to use reduce for ...
3
votes
1answer
86 views

Tree-like nesting of function

Is there an elegant way to nest a function in a similar fashion to tree graphs; i.e., create and follow branches until some criterion is met (until we reach a leaf)? An example: We want to ...
0
votes
2answers
122 views

How to find critical points of trig function over an interval?

I need to find the critical points (maxima, minima and points of inflection) of the function $f(x)= \sin(x)+\ln(\frac{1}{4}x^2-\frac{1}{4}x+\frac{3}{2})$ over the interval $-3\leq x\leq5$. To do this ...
2
votes
1answer
88 views

How to solve for the closed form of this recurrence?

For integers $L,k \geq 0$: $$T(L,k) = \begin{cases} 0 & \text{if }k \geq d, \text{ever}\\ -a_{k} & \text{if }L=0 \text{ and } k<d\\ a_dT(L-1,k+1) - a_{k}T(L-1,0)& \text{if } L>0 ...
1
vote
2answers
203 views

Problems finding intersection points between line and generic function

I'm trying to find Intersection points between a line, which is given by 2 points, and a generic function (I want it to be able to handle polynomial functions, circles/ovals, lines and all ...
0
votes
0answers
86 views

Plotting FindRoot solutions against one parameter, varying another

I'm writing my question wholly anew as it has changed its form a bit and I've got some actual code attached as well. I've got a system of equations for which I find numerical solutions with FindRoot. ...
3
votes
1answer
104 views

How can I solve my easy system of equations?

I am new to Mathematica and am afraid this is a silly question. I have this very easy substitution, it has three equations on three unknowns {w1, l1, t1}. I want to ...