Assistance with math please?

Question

Find the domain for the particular solution to the differential equation , with initial condition y(2) = 2.

Options:

1)	x > -2
2)
3)	[-4, 4]
4)	All real numbers

Answer 1

dy/dx = -x/y

Separate variables to get ydy = -xdx

Integrate both sides with respect to x and obtain (1/2)y² = -(1/2)x² + C

So, y² = -x² + C

y = 2 when x = 2, so 4 = -4 + C. Thus, C = 8

y = √ (8 - x²)

Domain: { x l 8 - x² ≥ 0)

So, x² ≤ 8

Answer: [-√8, √8] = [-2√2, 2√2]