6 The variables \(x\) and \(y\) satisfy the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + 3 y = 2 x + 1$$
Find
- the complementary function,
- the general solution.
In a particular case, it is given that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\) when \(x = 0\).
- Find the solution of the differential equation in this case.
- Write down the function to which \(y\) approximates when \(x\) is large and positive.