What is the particular solution to the differential equation d y d x = x − 2/y^2 with the initial condition y ( − 2 ) = 3 ?

Answer 1

As you have written it, I suspect the equation has no easy solution.

But I think you mean dy/dx = (x-2)/y² and you should have used parentheses as I did to make absolutely clear what you mean.

If I am correct in my thinking about what you mean, then variables are separable and your solution will have 2 easy integrations and I constant.