Questions tagged [parametric-functions]

Questions about explicit functions expressed in terms of independent variables, i.e. parameters. Including approaches for rewriting functions using different parameterizations.

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How to impose a change of variable in a differential equation?

I have this differential equation in terms of the variable $y$ deq[y_]=y^2 U''[y] + (a y^2 + b y + c) U'[y] + (d y + f) U[y]=0 and I want to make the change of ...
PhysFan's user avatar
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Is it possible to get rid of `Root` and have an explicit closed-form solution for the given equation?

I want to solve the given equation for m>0 where all parameters are Reals and a<0. ...
PhysFan's user avatar
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2 votes
1 answer
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Maximize a function of $x$ and $y$ where $x^2 +y^2 \leq 1$

I have the following function: $f(x,y) = x(y^2-x^2)- \frac{(x^2 +y^2)^2}{2\rho}+\frac{3x^2(y^2-4x^2)}{\rho}$ where $\rho>0$ is a constant. My goal is to find the maximum value of this function ...
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Cassini oval plotting related isues

PART 1 The parametric equation mentioned in the webpage, Eggs, melons, and peanuts - Cassini Oval, for the Cassini oval is given by ...
user444's user avatar
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1 vote
1 answer
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Plotting a parameteric function

I aim to plot the amoeba of f=x1^3 + x2^3 - 4 x1 x2 + 1 . Following this thread, I have solved f==0 and tried to plot the log of ...
Shasa's user avatar
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7 votes
3 answers
400 views

How to plot a surface given implicitly by 3 equations in 5 coordinate variables?

I have 3 implicit equations in 5 variables: $f_1(S, y_h, y_d, x_h, J)=0$, $f_2(S, y_h, y_d, x_h, J)=0$, and $f_3(S, y_h, y_d, x_h, J)=0$. These equations determine a 3D surface in $S-y_h-y_d$ ...
yuhao chen's user avatar
3 votes
1 answer
154 views

Finding the parametric equation of two intersecting surfaces

I was given two equations of surfaces: an ellipsoid (x/2)^2+(y/4)^2+(z/5)^2=1 and a plane z=3. So I graphed their intersection ...
bb_823's user avatar
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3 votes
2 answers
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Area of ​a parametrically defined function

I can’t solve the problem; I need to find the area of ​​a parametrically defined function. According to the graph, part of the area has a negative sign. ...
Vladimir's user avatar
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Get curve equation from parametrization

I am quite new to Mathematica and I have been wondering how to do this one very specific thing. I have two functions $x(t)$ and $y(t)$ that are the parametrization of a curve, how would I get the ...
Memat's user avatar
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2 votes
2 answers
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Convert list of variables to list of parametrized functions

I have a list of differential equations of some variables eqns = {f[x,y,x',y'],g[x,y,x',y']} e.g., f[x,y,x',y'] = x x' + y y'. ...
Joalito's user avatar
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Plotting function defined via NIntegrate is too slow

I have the following functions as solutions of a system of differential equations (for calculation, I used ParametricNDSolveValue) ...
derdin1's user avatar
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1 answer
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Speed Up Plotting of Mathieu Equations

I am trying to plot Mathieu Functions, running for an hour without a result. Here is my code: First define the relevant physical constant: ...
ZHENGYAO HUANG's user avatar
4 votes
3 answers
303 views

Plotting multiple parametric 3D curves without using the Show command

How can I plot multiple parametric 3D curves on a single graph without the need to combine them using Show? Additionally, is there a way to clearly distinguish ...
emnha's user avatar
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1 vote
1 answer
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How to invert this function when the argument e is small?

I need to find an analytical solution the following equation for e in terms of n and p ...
Dotman's user avatar
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2 votes
4 answers
111 views

Plot the surface $xy+z=1$, plane $x+y+z=1,$, and their curve of intersection in different colors

Plot the surface $x y + z = 1$, plane $x+y+z=1$, and their curve of in intersection in different colors.
Parker James's user avatar
3 votes
1 answer
225 views

Parametric Plotting 6D Dimensions to 3D for Visualizing a Solution

I am trying to find out when: $$f(x,y,z,α,β,γ):= z\cos(β)\cos(γ)+y(\cos(γ)\sin(α)\sin(β)+\cos(α)\sin(γ))+x(−\cos(α)\cos(γ)\sin(β)+\sin(α)\sin(γ)),$$ where $α,β, \text{and } γ$ can be any value in $[-2\...
Teg Louis's user avatar
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ParametricNDSolve with known solution at one limit

The ODE I wish to understand is the following: ...
Anthony's user avatar
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2 votes
1 answer
136 views

Convert R code to Mathematica code of Poisson log-likelihood for the epidemic curve

I want to define a function that simulates the model for a given combination of parameters and calculates the Poisson log-likelihood for the epidemic curve of reported cases: ...
Athanasios Paraskevopoulos's user avatar
1 vote
0 answers
50 views

Stiffness problem which abruptly stops the evaluation

We have a Lagrangian and we found the EOM. We need to solve the EOM and find the Phase-space plot. However, we are facing a stiffness problem which abruptly stops the evaluation (...
user444's user avatar
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Find parameters in an SIR model

...
Athanasios Paraskevopoulos's user avatar
-5 votes
3 answers
103 views

Why can't the problem of constancy be solved?

Clear["Global`*"] f[x_] := a E^x - Log[x] ForAll[x, 1 < x < 2, f'[x] > 0] Resolve[%, Reals] Why can't the problem of constancy be solved?
csn899's user avatar
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3 votes
2 answers
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Given the parity of a function, how can I find the value of a parameter?

Given that the function g [x] is an even function g[x_] := (x + a) Log[(2 x - 1)/(2 x + 1)] How to find the value of parameter a? I tried the following method but ...
csn899's user avatar
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3 votes
3 answers
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How to find the range of values for this absolute value function?

The function is: f[x_] := Abs[2 x - k] + Abs[2/k x + 1/k^2] The range of parameter k is: 0 < k <= 1 How to find the ...
csn899's user avatar
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2 votes
1 answer
100 views

Eigenfunction condition of time-independent Schrödinger equation

I'm trying to get the eigenfunctions and eigenvalues of the following one-dimensional Schrodinger equation: $$ -\frac{1}{2}\frac{d^2}{dx^2}\psi(x)+V(x)\psi(x)=E\psi(x)\,,$$ where the external ...
Crazydemon92's user avatar
1 vote
3 answers
251 views

Finding maximum value of a function with parameter

How can I find the maximum value (and the corresponding $x$) of the following function with parameter $t$: $$ f(x) = |x^2-tx + 2t|$$ on a closed interval $x\in[0,1]$? I tried using ...
csn899's user avatar
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3 votes
2 answers
175 views

Complicated system of two non linear equations in three variables

I have a system of two equations in three variables. The two expressions involved in the system are obtained diagonalizing the following matrix with Eigensystem[]: <...
Anna's user avatar
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1 vote
1 answer
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Fitting Parameters to the Heat Equation [closed]

As part of my research, I have been trying to use a model of heat conduction through a 2D layer given an input steady-state Gaussian power profile and a heat loss term to the environment. All but one ...
Jack LeGrow's user avatar
3 votes
1 answer
170 views

Is it possible to ask Mathematica to obtain the function describing the upper and lower boundaries of a combinations of functions?

Assume that I have three one-variable non-periodic functions $f(x),g(x),h(x)$ for $x>0$. The question is: is it possible to ask Mathematica to obtain the function describing the upper and lower ...
math2021's user avatar
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Find the fitting values of unknown parametres by ParametricNDSolveValue

I have this ODE: eq = E^(2 a x[t]) + (2 + 13 E^(2 (a - b) x[t]) x'[t]^2== 6 a E^(2 (a - b) x[t]) ((2 a - b) x'[t]^2+ x''[t] ) I want to solve for ...
Dr. phy's user avatar
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2 answers
89 views

Number of solutions of an equation with parameter (Mathematica)

Some nonlinear equations can have many solutions for a given parameter and I would like to know how the number of solutions varies with respect to a parameter $a$. I would like to solve: $ax^2+x-1=e^...
Jakub Wróbel's user avatar
0 votes
0 answers
146 views

Factorization of 5th polynomial with Wolfram-Mathematica

I have a very complicated 5th-degree polynomial form. Using the factor function in Wolfram is impossible to make it because of the high degree. I just want to know that is it possible to factor as I ...
analog_designer's user avatar
3 votes
3 answers
168 views

Parametric Plot in different graphs

i would like to plot the function of a parametric differential system below ideal in separate graphs. My code is ...
Agaph's user avatar
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5 votes
3 answers
166 views

How to use plot parametric function with discrete data?

You can easily create a ParametricPlot using the syntax ParametricPlot[{fx, fy}, {t, tmin, tmax}] when you have the functions fx ...
internet's user avatar
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2 votes
1 answer
184 views

How to plot Hyperbolic using parametric form with Animation?

Animate[ ParametricPlot[{Cos[\[Theta]], Sin[\[Theta]]}, {\[Theta], 0, a + 0.0001}, PlotRange -> {{-1, 1}, {-1, 1}}], {a, 0, 2 Pi}, AnimationRunning -> False] ...
CasperYC's user avatar
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3 votes
1 answer
82 views

Manipulating expression ParametricPlot

How can I make Mathematica plot the curve being traced by the focii of the ellipse? I know the traced curve would be drawn in an instant, when I switch the variable from u to t, but I want the curve ...
LLCJ's user avatar
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1 vote
1 answer
87 views

Plot of non-homogeneous diffusion equation

Let the initial and boundary value problem for the diffusion heat equation \begin{align*} u_t(x,t)&=u_{xx}(x,t)-\alpha u_x(x,t), \quad 0<x<+\infty,t>0\\ u(x,0)&=f(x), \quad x\...
Athanasios Paraskevopoulos's user avatar
0 votes
1 answer
33 views

Is it possible to ask Mathematica to order this expression in terms of descending absolute values of the arguments of the exponential functions?

I have the given expression which is a sum of exponential functions with some parameters $a,t,u,y$ where $a>0$. Question Is it possible to ask Mathematica to order this expression in terms of ...
Martha97's user avatar
  • 349
6 votes
6 answers
843 views

How to wrap a cylinder?

i'm trying to wrap a cylinder in a torus, the best i've done is the following code: ...
Oscar Hernández's user avatar
0 votes
1 answer
46 views

Unable to access solutions of coupled linear differential equations using ParametricNDSolve [closed]

I have the following code that tries to solve for 4 coupled differential equations Ap1[x], Ath[x], ...
kowalski's user avatar
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0 votes
2 answers
70 views

Accessing solutions of coupled differential equations solved using ParametricNDSolve [closed]

I have the following linear coupled differential equations (y , z) that I wish to solve with a varying parameter a ...
kowalski's user avatar
  • 375
2 votes
1 answer
81 views

Why does Series give two different results for given function?

I want to do Series of this function x^12 Cos[y x]^2 Sin[y x]^6 Sin[(-1 + Sqrt[3]) y x]^2 around ...
Martha97's user avatar
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0 votes
0 answers
33 views

ParametricNDSolve Skipping Over Periodic Input Function

I am attemting to model some expermental data with the differential equation $\frac{dm}{dt} = D(m) + F(\omega t)$ via Mathematica's ParametricNDSolveValue function. ...
Professional Nerd's user avatar
1 vote
1 answer
181 views

Solving Helmholtz Equation in 2D for Circular Disk with DEigensystem, NDEigensystem

I would like to solve the Helmholtz equation with Dirichlet boundary conditions in two dimensions for a circular disk with a radius of 1. $\Omega =$ some boundary e.g. a circle $ \nabla^2 u(x,y) + k^...
Athanasios Paraskevopoulos's user avatar
1 vote
1 answer
138 views

Helmholtz Problem in Circular Disk

The following expression $$u_{nm}(r,\theta)=J_n(x_{nm}\frac{r}{a}) \begin{cases} \cos n \theta, & n=0,1,2 , m=1,2 \\ \sin n \theta, & \end{cases}$$ gives the solution for the Helmholtz ...
Athanasios Paraskevopoulos's user avatar
4 votes
5 answers
321 views

Error when trying to plot a folium

I am working on my assigment in Mathematica and I get this weird error when trying to plot the graph (folium) with tangent lines. ...
Jakob's user avatar
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1 vote
1 answer
84 views

Solving a complicated equation of order 5. completely parametrically

I have this equation and it takes so much time to solve. i would appreciate some guidance how to solve it. 0<l<1 and 0<gamma<1 and -Pi/2<theta<Pi/2 and w is real and positive. other ...
Ali Taher's user avatar
0 votes
0 answers
24 views

Minimizing 2-variable function with underdetermined constraint

I'm trying to minimize the function eps wrt the real variables a1 and a2, making sure that ...
Freestyla's user avatar
1 vote
0 answers
71 views

Is there any documentation for vibration and solid mechanics research via Mathematica? [closed]

I am interested in the solid mechanics (elastic mechanics and structural mechanics, etc.), and vibration, is there any material or documentation in this aspect via FEM in Mathematica?
fhrl's user avatar
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1 answer
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Can someone please explain where I am going wrong in the given argument? Is it obvious that $f(m,s)>0$?

I have a two-variable function $f(m,s)$ for real $m>0$ and $s>0$, and as the first picture shows, it seems that it is always positive; on the other hand, I can easily find the minimum of $f(m,s)$...
Martha97's user avatar
  • 349
2 votes
1 answer
222 views

How to parameterize a pyramid with a square base?

I wanted to parameterize and draw a pyramid with a square base. The base was parameterized as a function of t , getting: ...
Sara's user avatar
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