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

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0answers
70 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
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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
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1answer
51 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
120 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 ...
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2answers
40 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
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1answer
114 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 ...
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0answers
49 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
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1answer
174 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
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1answer
86 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
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0answers
27 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
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1answer
32 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
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0answers
41 views

Solving Lagrangian (4 vars to solve for)

I'm a bit new to Mathematica, but here's what I've got: ...
0
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0answers
69 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
66 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
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1answer
80 views

Complicated equation solving

I want to find the maximum point or optimal value $y$ of Rx1[y_, a_, b_]. ...
2
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1answer
80 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
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0answers
24 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
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2answers
63 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
82 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
114 views

Can Mathematica solve this type of recurrence?

I have the following recursively defined equation: ...
1
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3answers
136 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
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0answers
57 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
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1answer
51 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
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1answer
64 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 $z$
1
vote
1answer
61 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
127 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
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1answer
99 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
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0answers
35 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
95 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
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2answers
181 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
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1answer
46 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
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0answers
51 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
82 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
108 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
83 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
143 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
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0answers
68 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
102 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 ...
0
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0answers
32 views

Issue with FindRoot and initial value

I have a quite unwieldy function and I would like to obtain a root via FindRoot. ...
1
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4answers
143 views

Solve reports it can't handle my equation

I am trying to solve the following equation Solve[x ϵ + (-ϵ) x^-ϵ - c (-ϵ) x^(-ϵ - 1) == 0, x] Yields Solve::nsmet: This system cannot be solved with the ...
2
votes
0answers
46 views

How to handle solution returned by ParametricNDSolveValue in FindRoot

i was trying to solve a problem relative to root finding in a system of differential equations; here's a simpler case. With two distinct set of parametric differential equations, i'm able to find the ...
1
vote
1answer
194 views

4th-order Runge-Kutta method to solve a system of coupled ODEs [duplicate]

I am a beginner at Mathematica programming and with the Runge-Kutta method as well. I'm trying to solve a system of coupled ODEs using a 4th-order Runge-Kutta method for my project work. I have ...
0
votes
2answers
173 views

Defining the domain of positive real numbers

I am trying to solve an equation by assuming that all the variables are real and strictly positive. I can use the keyword Reals for the argument ...
0
votes
1answer
59 views

FindRoot, Loops and multivariate nonlinear system

I posted a question yesterday asking how I could get all the solutions to my system of 4 nonlinear equations with 4 unknowns. I gave up on this since it seems ...
1
vote
0answers
51 views

Why am I getting a conditional output when importing the Dirac Equation to Mathematica? [duplicate]

Just starting out with Mathematica and trying to use the Dirac Equation. I'm working with the following form of the Dirac Equation: $$ i \hbar \gamma^\mu \partial_\mu \psi - m c \psi = 0 $$ And my ...
0
votes
1answer
97 views

Eliminating parameter from parametric equation

In Mathematica Online I tried: Eliminate[{x == t + t^3, y == t - t^3, z == 1 + t^4}, {t}] ...
0
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0answers
47 views

Any way of solving this system of nonlinear equations with non integer powers?

I have a system of four nonlinear equations. Some of the exponents are fractions. I was wondering if this is what is causing NSolve to run for hours without giving ...
1
vote
2answers
69 views

Confusion in Numerical Integration while using FindRoot

I used this code for numerical integration NIntegrate[(x^2 - .0015 x^4)/D[(x^2 - .0015 x^4), x], {x, 1.414, 13}] when upperlimit of x is 13, the integral value ...
0
votes
1answer
75 views

Solving a single-variable equation mixed with exponential and algebraic

Trying to solve for x Solve[((a - 1) (1 + d x^2))/(a (Exp[b x + c] - 1)) - e == 0, x] in terms of the constants a,b,c,d, and e. Mathematica says "This ...