# I just reverse-engineered this

Calculus Level 4

$\large \frac{dy}{dx} = \frac{ y^{2 - \frac{1}{y}}}{ 1 - \ln \: y}$

Given that the above differential equation has its solution passing through $$(1, 1)$$. Find the corresponding value of $$x$$ when $$y = e^{\frac{1}{e}}$$. Input your answer as $$\lfloor 1000x \rfloor$$.

You may use a calculator for the final step of your calculation.

Clarifications:

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