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

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1answer
83 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
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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
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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
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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
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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
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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
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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
82 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
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2answers
142 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
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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
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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 ...