Questions tagged [implicit]

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How to plug in an implicit function into another function and evaluate in Mathematica? [closed]

I am wondering how to do the following in Mathematica. Say, we have an implicit function $y=f(x)$ defined by $F(x,y)=0$. I would like to evaluate another function $G(x,y)$ at the implicit function $y=...
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Find implicit function from [closed]

I'm trying to find implicit function. I have four parametric equations for functions T := T[x,y,z] X := X[x,y,z] Y := Y[x,y,z] Z := Z[x,y,z] And I want to find a ...
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2 votes
2 answers
60 views

How to draw sectional plot for a 3D parameter equation?

How to draw sectional plot for a 3D parameter equation? Firstly, the MMA code is given as ...
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6 votes
2 answers
437 views

Compare MMA program with MATLAB program by plotting the same equation

Cross-posted in Wolfram Community. Firstly, the MATLAB program is ...
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2 votes
3 answers
157 views

Solving implicitly a trigonometric equation

I am trying to solve this equation with respect to L: L== ((9.81*T^2)/(2*Pi)) Tan[2Pi*d/L] Since you have the unknown ...
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3 votes
1 answer
126 views

A system of ordinary differential equations is being recognized as a DAE

I want a function auxiliarfunction that depends on two variables: ρh and ν. I need to plot ...
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1 answer
115 views

Problem with NDSolve regarding initial conditions of the derivative of a parametric function

I have a function functiontoplot defined using the following piece of code: ...
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1 answer
83 views

Branches of a curve defined implicitly

I have the variable functiontoplot, defined using the following piece of code: ...
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0 answers
120 views

Plotting a curve defined implicitly

I have defined the function functiontoplot using the following piece of code: ...
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1 vote
0 answers
79 views

Implicit function in an ODE when using DSolve

I'm trying to solve an ODE with DSolve. The problem I'm facing is that in the ODE there appears an implicit function of the variable r*. The equation I'm trying to solve is ...
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4 votes
3 answers
253 views

Plot the intersection of random half-spaces

The code ...
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2 votes
1 answer
84 views

Problems plotting ImplicitRegion

I have run into some rather strange behavior regarding plotting over regions defined by ImplicitRegion. I have a condition given by ...
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4 votes
1 answer
102 views

Imaginary variables in ImplicitRegion

I am using the function ImplicitRegion[]. RegionPlot[ImplicitRegion[x^2 + y^2 == -1, {x, y}]] which gives me a circle, though in the documentation variables are ...
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3 votes
0 answers
111 views

Sweep, scale, and rotate implicit 3d region or contour plot along an arbitrary curve

Suppose I have a 3d region or contour that is implicitly defined and has no explicit parameterization. This is easy to plot, as RegionPlot3D and ContourPlot3D allow implicit functions. But now I want ...
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1 vote
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117 views

Finding the arc length of a region defined implicitly with an interpolated function

I begin by defining an interpolation of some data I have stored at this link for brevity. The interpolating function is a function of two variables, x and ...
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1 vote
1 answer
92 views

Composition of implicit functions

Let me explain what i have been doing so far. So I want to find an numerical solution or at least a grafic solution to this equation: ...
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1 vote
0 answers
50 views

DSolve: lack of implicit option (unlike Maple's dsolve built-in option)

I am working with the book 'Differential Equations for Engineers' (Cambridge University Press). The author dedicates one chapter of the book in solving ODEs with Maple. The book was published in 2010. ...
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1 vote
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How do I plot two normalized variables with one varying parameter as a 2d plot or a contour plot?

I'm trying to replicate a plot that has both (x,y) normalized variables, I've tried using Evaluate and Contourplot with no success. I have set Rn=20, but it should be another variable. Where Fn=fs/fr, ...
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1 vote
1 answer
85 views

Improve performance of evaluating over an implicit region

Consider the following implicit region: ...
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0 votes
2 answers
86 views

Implicit differentiation such that I an numerically solve an equation [closed]

If I have some function: N(t) = N0e^(bt) where b is a function of N(t). How do i calculate dN/dt? It gives me a recursion warning since it's just caught in a loop of substituting in N(t) into b over ...
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3 votes
3 answers
310 views

Plot involving an implicit function

I'm trying to make a plot that depends on an implicit function. This example illustrates the problem: plot $c=2l +n$ in the $c \times l$ axes, where $n$ is implicitly determined by $n^5+ 2n = c^2$. ...
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3 votes
2 answers
186 views

Solving the Shifted Neutral Axis Problem

Problem Description: In solving the "Shifted Neutral Axis" method for the stress distribution of a vertical steel vessel supported on a concrete foundation, we can derive the following ...
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2 answers
107 views

Plot implicit polar equation streamlines

I'm trying to plot streamlines of Stokes solution to an sphere, the expression of streamlines is I've seen similar questions before and this what I have tried As you can see, a=1, U=1, but it seems ...
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2 votes
0 answers
86 views

Large system of implicit differential equations

We are trying to solve a large system of implicit system of differential equations for complex variables $\boldsymbol{\alpha}\left(t\right)$ and $\boldsymbol{\lambda}\left(t\right)$. System consists ...
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3 votes
1 answer
242 views

Solve transcendental equation involving a built-in function [closed]

How can I solve an equation of the following form? $$x = 10+\mathrm{\mathbf{PrimePi}[x]}$$ where $x$ is an integer. I am using Solve but am getting the following ...
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1 vote
2 answers
80 views

Interval arithmetic and implicit function inside test

I has implicit function and square region. I need to check this region for presence of part of curve, with interval arithmetic only. My attempt: ...
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3 votes
1 answer
438 views

Can we convert any parametric equation to implicit form?

The Archimedes spiral equation in parametric form: fx[t_] := Cos[t]*t; fy[t_] := Sin[t]*t; How can it be converted to implicit form? Is there a general method ...
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10 votes
1 answer
1k views

How can I find a parametric equation for an implicit surface?

I need a parametric equation for the Taubin heart surface, which is defined in implicit form. I asked a similar question in math branch, but didn't get an answer. This is the implicit form: $$\\\...
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0 votes
1 answer
38 views

How to plot the absolute values of the solutions to a parametric equation versus the parameter?

Mathematical formulation of my problem: Let $\Theta\subset\Bbb R$ be an interval. For each $\theta\in\Theta$ let $f_\theta: \Bbb C\to\Bbb C$ be some function and $z_{\theta,1},\ldots,z_{\theta,n(\...
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1 vote
1 answer
118 views

Solve implicit equations, input and plot the solution in a different equation

I have two implicitly defined variables, $\sigma_D$ and $\sigma_M$ one of which is a function of the parameter $v$. In particular, $\sigma_D = F(\sigma_D,v)$ where $F(\sigma_D,v)=0$ if $ c_D < -0....
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1 vote
1 answer
193 views

How to get the implicit solution of this PDE (Maple can but I don't manage with mathematica)?

I asked this question about the analytical solution of the PDE: $$\partial_t c=\partial_x((c-a)(c-b)\partial_xc) $$ And I was given the answer that Maple gives the following implicit form as a ...
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0 votes
1 answer
45 views

How can I get paired coordinates from the implicite function?

I have equation E^y = x. How can I use Mathematica to solve all of "y" from the desired "x" value. For example, I want to solve for "y" from x = 0.5 , 1 , 1.5 , 2 , .... , 9.5 , 10. The solution ...
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2 votes
2 answers
151 views

Solve implicit equations and plot solutions as parameter changes

I have the following two implicit equations that are functions of a parameter $f \in (.5,1]$. I would like to solve these two equations (i.e get $\sigma_D$ and $\sigma_M$) for different $f$ values and ...
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1 vote
1 answer
76 views

Determine inverse function with Gröbner basis

I am trying to generalize a way to invert a function using Gröbner basis. My functions are defined in the following form: ...
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0 votes
1 answer
338 views

Implicit Function Theorem

I think I am stuck here right now: The exercise is to use implicit differentiation to determine y' considering the following equation: I managed to do this with: ...
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8 votes
2 answers
1k views

How to plot a surface from a system of equations? [duplicate]

It seems like a natural thing to do, however I can't seem to find anything on the docs nor here on SE. What I'd like to plot is the locus of solutions to a system of (polynomial) equations, e.g. $$\...
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0 votes
0 answers
61 views

How to Solve a Differential Equation System Depending on Variable Solved in an Implicit Function?

I have an ordinary differential equation system need to be solved by using Mathematica. $\frac{dk(t)}{dt}=((1-\kappa(t))k(t))^{\alpha}(1-\frac{\kappa(t)}{\kappa(t)+\frac{1-\alpha}{\alpha}\frac{\eta}{\...
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5 votes
2 answers
192 views

Holes in ElementMesh with ToElementMesh of ImplicitRegion

I am trying to plot a function in a region below a level curve of the function and within a cell. I have been doing this by calculating an ElementMesh using ...
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3 votes
2 answers
344 views

Plot implicit region in 3D not working

I'm having troubles plotting an implicit region R (the full expression will be given at the end of this message for sake of readability). This implicit region R is defined by both inequalities and ...
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2 votes
2 answers
206 views

Multivariate series for approximating implicit system

I'm trying to approximate the solution of an implicit set of equations by means of a Taylor series. I have managed to do so for a solution expressed in terms of a single independent variable, by using ...
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0 votes
0 answers
129 views

Implicit derivative of set of equations

I have an equation and I want to take its derivative with respect to two variables. However, it contains some parameters which need to solve them together to find them (Pn, omega, gamma). These ...
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2 votes
4 answers
242 views

Printing values of y for a range of x for an implicit function f(x,y)

I want to print the values of y for a range of x for an implicit function f(x,y). My equation is f(x,y)=x^2+y^2+2. The range of x is (2,10). I want the corresponding values of y.
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1 vote
1 answer
229 views

Implicit and Parametric Plot

I am trying to graph the partials of two equations with respect to t, with both equations being implicit. I know I should be getting ellipses with the x-axis as the major axis. ...
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8 votes
1 answer
228 views

ElementMesh from ImplicitRegion cuts corners of region

I'm trying to define a region within a cell and below a level set of a function using ImplicitRegion and ToElementMesh. Here I ...
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0 votes
2 answers
204 views

How to compare ImplicitRegion with empty region?

I have the following function using ImplicitRegion: ...
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0 votes
1 answer
338 views

How to ContourPlot a two variables (x,y) implicit function with y normalized?

I am trying to use ContourPlot to plot an implicit function. Now I have two variables (x,y) implicit function: ...
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2 votes
2 answers
70 views

Plot f(x,g(x)) where u(x,g(x))=0 can not be solved explicitly

Suppose $u(x,g(x))=0$ can not be solved explicitly for $g(x)$. I need to plot $f(x,g(x))$. How can this be done? An example: $\frac{1}{\log y}=y-x$ for $x\ge 1$ has a solution for $y$, but can not be ...
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2 votes
2 answers
83 views

Incorrect implicit region for function that indexes or sorts a list

I'm having trouble creating a region with ImplicitRegion. In general, I first limit the region to be within a Parallelogram. <...
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0 votes
0 answers
67 views

Mathematica giving incorrect result for implicit equation $x^{\frac{2}{3}} + y^{\frac{2}{3}} = 1$? [duplicate]

When I type the following implicit equation into Mathematica I only get 'one quarter' of what the resulting plot should look like, i.e., I only get the upper-right quadrant. ...
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1 vote
2 answers
455 views

3D plot over an implicit region gives no answer

I have a function(X,Y) which I would like to plot over an implicit region. ...
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