4. (a) Show that the substitution \(y ^ { 2 } = \frac { 1 } { z }\) transforms the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } + 2 y = 3 x y ^ { 3 } \quad y \neq 0$$ into the differential equation $$\frac { \mathrm { d } z } { \mathrm {~d} x } - 4 z = - 6 x$$ (b) Obtain the general solution of differential equation (II).
(c) Hence obtain the general solution of differential equation (I), giving your answer in the form \(y ^ { 2 } = \mathrm { f } ( x )\)