Final answer:
To solve the differential equation, (1) separate the variables, (2) integrate both sides, and (3) incorporate the constant of integration. The solution is y = ln|x(x-2)| + C.
Step-by-step explanation:
To solve the differential equation (dy)/(dx) = (2x-6)/(x^2-2x), we can rewrite it as (dy)/(dx) = (2x-6)/(x(x-2)).
Then, we can separate the variables and integrate both sides. This gives us ∫dy = ∫(2x-6)/(x(x-2)) dx.
Once we integrate, we find y = ln|x(x-2)| + C, where C is the constant of integration.