Solve: xy' + y = x^4y^3
y' + y/x = x^3y^3
y'y^-3 + (y^(-2))/x = x^3
v = y^-2
dv/dx = -2y^-3(dy/dx)
sub
(-1/2)dv/dx + (1/x)v = x^3
dv/dx + (-2/x)v = -2x^3
int factor = 1/x^2
multiply and integrate
(1/x^2)v = -x^2 + c
v = -2x^4 + Cx^2
y^-2 = -2x^4 + Cx^2

Is it right and is it typical to leave these as a function of y^-2 ??
Its my first one so be gentle. Thanks.