Inverse derivation of differential equation $f(x)=\frac{dy}{dx} +\frac{d^2y}{dx^2}+\frac{d^3y}{dx^3}$

Question

The following function is given: $$ f(x)=\frac{dy}{dx} +\frac{d^2y}{dx^2}+\frac{d^3y}{dx^3}$$

I'am looking for the inverse function in Leibniz writing style. Here is my attempt:

$$ f^{-1}(x)=\frac{dx}{dy} -\frac{d^2x}{dy^2} {\Biggl(\frac{dy}{dx}}\Biggl)^3 -\frac{d^3x}{dy^3} {\Biggl(\frac{dy}{dx}}\Biggl)^4+3{\Biggl(\frac{d^2x}{dy^2}}\Biggl)^2 {\Biggl(\frac{dy}{dx}}\Biggl)^5 $$

Is this correct?