Exercise

1. Solve the following differential equation using the variation of parameter.
$$\begin{array}{ll} (a) \ y^{\prime\prime} + 2y^{\prime} + y = ... ...) \ y^{\prime\prime\prime} + y^{\prime} = \tan{x} & \end{array}$$
2. Using the variation of parameter, show the general solution of $y^{\prime\prime} + y = f(x)$ is given by

$$y = c_{1}\cos{x} + c_{2}\sin{x} + \int_{a}^{x}f(t)\sin{(x-t)}dt$$