# 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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### ParametricNDSolveValue, NMaximize: Dealing with complex results in maximization problem

I analyze a system of differential equations in several variables including mus[t], mui[t], and w[t]. Time runs from t=0 to t=T. The two initial values mus[0] and mui[0] can freely be chosen; their ...
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### Expand a 2d curve into a 3d path curve with a fixed axis of rotation?

Given a string of fonts, such as "ABC", give a space line, how to rotate around the line while expanding the string into several curves.
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### How can I simplify this out put?

Based on this answer, I tried to find the condition to function $y = \dfrac{a x+ b}{c x +d}$ where $ad \neq 0$ and $a d - b c \neq 0$ increasing on $(-d/c, +\infty)$. I tried ...
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### How can I find values of m so that the function $\frac{-m+x^2+x-4}{4 x-m}$ increasing in the interval $(1,2)$?

I am trying to find value of marameters $m$ so that the function $f(x) = \dfrac{-m+x^2+x-4}{4 x-m}$ increasing in the interval $(1,2)$? I tried ...
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1 vote
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### Iterated integral numerically

I am trying to calculate a double integral. However, after a long time, Mathematica does not give me any outputs. Has someone any ideas how to calculate this? ...
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### Issue with Integration of a Parameter-Dependent Function in Mathematica [closed]

The following Mathematica code is given: ...
1 vote
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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 ...
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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. ...
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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 ...
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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 ...
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### 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 $S-y_h-y_d$ ...
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### 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 ...
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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. ...
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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 ...
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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'. ...
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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) ...
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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: ...
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### 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 ...
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1 vote
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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 ...
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### 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.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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] ...
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### 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 ...
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1 vote
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### 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\...
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### 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 ...
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### How to wrap a cylinder?

i'm trying to wrap a cylinder in a torus, the best i've done is the following code: ...
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### 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], ...
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### 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 ...
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### 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 ...
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### 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. ...
1 vote
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^...
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 ...