Question

Solve the differential equation.
(dy)/(dx)=(2x-6)/(x²)-2x)

Answer 1

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.