I need help with the integration of this dy/dx = x - 2y/x

i tried to take help from ai but this is what ir proved 💀

The correct answer is (3) (-1,2).

Given the slope of the tangent at any point (x, y) on the curve as (x²-2y)÷x, we can write the differential equation:

dy/dx = (x²-2y)/x

We are also given that the curve passes through the point (1, -2). We can use this information to find the equation of the curve.

Separating the variables, we get:

∫dy = ∫(x²-2y)/x dx

Integrating both sides, we get:

y = (1/3)x³ - 2x + C

Using the point (1, -2), we can find the value of C:

-2 = (1/3)(1)³ - 2(1) + C

C = -4/3

So, the equation of the curve is:

y = (1/3)x³ - 2x - 4/3

Now, we can check if the curve passes through the point (-1, 2):

2 = (1/3)(-1)³ - 2(-1) - 4/3

2 = -1/3 + 2 - 4/3

**2 = 2/3 (which is true)**

Therefore, the curve also passes through the point (-1, 2).