3
votes
1answer
76 views

Inverse Function Differential Equation [duplicate]

For the differential equation $$\frac{d}{dx}[y(x)]=y^{(-1)}(x)$$ where $y^{(-1)}(x)$ is the inverse of $y(x)$, find y(x). I gave up on finding the solution analytically pretty quickly and decided ...
3
votes
0answers
75 views

Is this a field of study?

Is there a name for an equation that takes the following form? $$F(f(x),f^{-1}(x),x)=0$$ A nice example being $$f(x)-f^{-1}(x)=0$$ because the solutions of this equation are their own inverses. ...
1
vote
1answer
18 views

Finding Inverse of Function With Two Instances of X

I need to find $f^{-1}(2)$ where $f(x) = 2 + x^2 + tan(πx/2)$ I know can substitute $f(x)$ with $y$ and swap $x$ and $y$: $$x = 2 + y^2 + tan(πy/2)$$ But I'm having trouble eliminating the tangent: ...
5
votes
3answers
393 views

Inverse function of $y=W(e^{ax+b})-W(e^{cx+d})+zx$

I have a simple question for which I am looking for a closed form expression (If there exits one). In other words, given: $$y=W(e^{ax+b})-W(e^{cx+d})+zx$$ where $W$ is the Lambert $W$ function and ...
1
vote
0answers
389 views

Finding inverse of function without knowing function?

This question has a programming application, but I thought it would be more appropriate (and educational) to ask here first and get some basic understanding. So my use-case will refer to some ...