First order differential equations (integrating factor)
5
Find the general solution of the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + \frac { y } { x } = \sin 2 x$$
expressing \(y\) in terms of \(x\) in your answer.
In a particular case, it is given that \(y = \frac { 2 } { \pi }\) when \(x = \frac { 1 } { 4 } \pi\).
Find the solution of the differential equation in this case.
Write down a function to which \(y\) approximates when \(x\) is large and positive.