- (a) Show that the transformation \(z = y ^ { \frac { 1 } { 2 } }\) transforms the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } - 4 y \tan x = 2 y ^ { \frac { 1 } { 2 } }$$
into the differential equation
$$\frac { \mathrm { d } z } { \mathrm {~d} x } - 2 z \tan x = 1$$
(b) Solve the differential equation (II) to find \(z\) as a function of \(x\).
(c) Hence obtain the general solution of the differential equation (I).
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