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Let $f$ be a function such that :$f:\mathbb{R}\to \mathbb{R}$ and $f^{-1}$ is a compositional inverse of $f$. I would'd like to know how do I solve this class of differential equation : $$\displaystyle \ f'= e^{\displaystyle {f}^{-1}}$$ ?.

Note 01: $f' =\displaystyle\frac{df}{dx}$.

Edit: ${f}^{-1}$ is the inverse compositional of $f$, for example $\log$ is the inverse application of exp function .

Note 02: I have edited my question to clarify the titled question that related to ${f}^{-1}$

Thank you for any help

Let $f$ be a function such that :$f:\mathbb{R}\to \mathbb{R}$ and $f^{-1}$ is a compositional inverse of $f$. I would'd like to know how do I solve this class of differential equation : $$\displaystyle \ f'= e^{\displaystyle {f}^{-1}}?$$

Note 01: $f' =\displaystyle\frac{df}{dx}$.

Edit: ${f}^{-1}$ is the inverse compositional of $f$, for example $\log$ is the inverse application of exp function .

Note 02: I have edited my question to clarify the titled question that related to ${f}^{-1}$

Thank you for any help

Let $f$ be a function such that :$f:\mathbb{R}\to \mathbb{R}$ and $f^{-1}$ is a reciprocal function of $f$ I w'd like to know how do i solve this class of differencial equation : $$\displaystyle \ f'= e^{\displaystyle {f}^{-1}}$$ ?.

Note 01: $f' =\displaystyle\frac{df}{dx}$.

Edit: ${f}^{-1}$ is the inverse compositional of $f$, for example $\log$ is the inverse application of exp function .

Note 02: I have edited my question to clarify the titled question that related to ${f}^{-1}$

Thank you for any help

Let $f$ be a function such that :$f:\mathbb{R}\to \mathbb{R}$ and $f^{-1}$ is a compositional inverse of $f$. I would'd like to know how do I solve this class of differential equation : $$\displaystyle \ f'= e^{\displaystyle {f}^{-1}}$$ ?.

Note 01: $f' =\displaystyle\frac{df}{dx}$.

Edit: ${f}^{-1}$ is the inverse compositional of $f$, for example $\log$ is the inverse application of exp function .

Note 02: I have edited my question to clarify the titled question that related to ${f}^{-1}$

Thank you for any help