Final answer:
To solve the given differential equation by separation of variables, integrate both sides after simplifying the integral.
Step-by-step explanation:
To solve the given differential equation by separation of variables, we need to integrate both sides of the equation. The differential equation is ∫ -(y - 6)² dx = 0.
First, we can simplify the integral by expanding the square term: ∫ -(y² - 12y + 36) dx = 0.
After integrating, we get -y³/3 + 6y² - 36y = C, where C is the constant of integration.