- (a) Show that the substitution \(y ^ { 2 } = \frac { 1 } { t }\) transforms the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + y = x y ^ { 3 }$$
into the differential equation
$$\frac { \mathrm { d } t } { \mathrm {~d} x } - 2 t = - 2 x$$
(b) Solve differential equation (II) and determine \(y ^ { 2 }\) in terms of \(x\).