First order differential equations (integrating factor)
5
Show that \(\tan x\) is an integrating factor for the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + \frac { \sec ^ { 2 } x } { \tan x } y = \tan x$$
(2 marks)
Hence solve this differential equation, given that \(y = 3\) when \(x = \frac { \pi } { 4 }\).
(6 marks)