# 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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### Defining parametric function resulting from DSolve

I am trying to define a function that is a solution of a simple ODE with a parameter, for example ...
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### How to get a specific component of an equation without hardcoding? [closed]

Say I define an equation line[t_] = {t, 2t, 3t}. What code will define x[t] = t, y[t] = 2t, ...
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### How to solve this set of PDE equations? I tried ParametricNDSolve, but

I am tring to solve set of PDE equations with parameters of v[z],q[z],T[z,t,r]. Below is my ...
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### How to make Sphere Transparent using ParametricPlot3D

This is the code I used Edit: This is the full code to create this image ...
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### Plotting Limit Cycle

I have Lotka Volterra Equations where the prey equation is modified. The Equations are x'[t]=a*x[t]*(1-x[t]/k)-b*x[t]*y[t] y'[t]=-c*y[t]+d*x[t]*y[t] To plot the ...
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### How to table ParametricPlot with parametric value

I can plot this code ...
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Writing: ...
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### Unpacking a Mathematica expression returned by DSolve

I was trying to solve a system of differential equations in Mathematica and had troubles understanding what the solution looked like. So I wanted help to unpack it. I had a system of two coupled ...
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### Singularity or stiff system in ParametricNDSolve

I have following parameters and equations(it's a complex one, please check it :) ): ...
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### Does mathematica cache the interpolating function from ParametricNDSolve?

I want to evaluate the solution of a system of non-linear ODEs using ParametricNDSolve. The output of ParametricNDSolve is a ParametricFunction object. Let's call it $f_\theta(t)$, where $\theta$ is a ...
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### Spheroidal Harmonics

There is a (scalar) field P varying on a spheroid (squashed) surface. This field is a function of four independent components ...
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### How to Create Lissajous Figures for Driven Damped Pendulum (as an animation/with Manipulate)

I wanted to know how can I generate a Lissajous plot for the forced driven pendulums (but for one pendulum in my case): (https://demonstrations.wolfram.com/ForcedPendulumsWithDamping/). I tried using ...
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### Converting a Non-Simple Closed Curve in an Image to a Parametric Equation

I would like to generate a parametric equation for a non-simple closed curve defined in a 2D image (shown below). This is the same problem as described in this question for simple curves. However, ...
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### How to solve integro-differential with parameters iteratively?

I am trying to solve an integro-differential equation and tried using one of the answers that I found in a related question: Numerically solve an integro-differential equation The difference is I have ...
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### Plotting multiple dependent variables with DSolve (projectile motion with air resistance)

I wrote a working code that plots what I need using DSolve and parametric plot. Here's an example of what it plots (and code is at the bottom). However, I want to be able to plot multiple graphs on ...
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### Issue with ParametricNDSolve and Table

I have a differential equation, I plot it for different initial values by using ParametricNDSOlve. Code - ...
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### NSolve with ParametricFunction

I have solved a SDE with ParametricNDSolve: s = ParametricNDSolve[ {p1, m1, p0, m0}, {P, m}, {r, 0, 1}, {m, k, e, Cnew} ] And now I want to treat the ...
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### Solving parametric ODEs at large parameter values

Question 101668 was not particularly clear and was put on hold for that reason. The author did clarify it a bit, but it seems unlikely that the question will be reopened. Through an exchange of ...
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### Plot with three functions and three parameters [closed]

I think my code doesn't have any problem but the program shows me this error and I'm confused! Plot::argr: Plot called with 1 argument; 2 arguments are expected. ...
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### Why does ParametricPlot does not reach the values I expect?

I have these expressions: ...
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### How can I substitute values into this set of equations?

I'm new to Mathematica and I'm trying to solve this set of trig equations (I'm not exactly sure if the syntax looks correct): ...