Final answer:
The equation dx/dy ≥ (y + 2) x sin x is a separable differential equation and can be solved by separation of variables followed by integration.
Step-by-step explanation:
The differential equation given is dx/dy ≥ (y + 2) x sin x. This is a separable first order differential equation, which we can solve by separating the variables: divide both sides by x and multiply both sides by dy to get (1 / x) dx = (y + 2) sin x dy. To find the solution that satisfies the initial condition y(0) = 2, we integrate both sides. This will give us the natural logarithm of the absolute value of x on the left side and an integral involving y and sine on the right side. The constants of integration from both sides are then solved for using the initial condition.