I have a problem that has eaten hours of my time. Each time I work it I get a different answer, which suggests it's an issue with algebra. Since I'm dysgraphic it's highly likely that I'm dropping negatives or making arithmetic errors.

Anyway, I need a step by step solution on this problem. Your solution will go into my notes on this section.

3(X^2)(Y^-2) + (X^-2)(Y^2) - (2X^-3) + ((6Y^-4) - 2(X^3)(Y^-3) - (2X^-1)(Y))Y' = 0, Y(1)=-1

This will need an integrating factor since M_x = 6XY^-2 -2X^-3Y^2 and N_y = -24Y^-5 + 6X^3Y^-4 -2X^-1 thus M_x is not equal to N_y. This is where things start going to heck for me!