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.