Is $\cos(x+y)=e^x$ an implicit function?

Question

I have tried separating the variables so as to find the answer. I had used the $\cos^{-1}(x)$ on both the sides and hence succeeded. However the answer given is that it is implicit. I searched on the internet and had got some mixed answers...Where did I go wrong?

Answer 1

$$\cos(x+y)=e^x$$ is an implicit equation, which can be made explicit as $$y=\arccos \left(e^x\right)-x$$

Note: Some, however, consider any equation that can be made explicit, not implicit. But, many of the seemingly implicit functions can be made explicit with varying degrees of efforts so it's pretty subjective.