Final answer:
The provided question is related to solving a non-linear differential equation, specifically in the form of dy/dx = y² + 4xy + 2.
Step-by-step explanation:
The question is asking to solve a differential equation dy/dx = y² + 4xy + 2x²/x². To solve this, we need to find a function y(x) that satisfies the equation. It's worth noticing that 2x²/x² simplifies to 2, simplifying our equation to dy/dx = y² + 4xy + 2. This equation appears to be a non-linear differential equation due to the y² term. A general method to solve such equations is beyond the scope of this response and would typically involve advanced techniques such as separation of variables, substitution, or utilizing a differential equations solving software.