ABSTRACT
In this chapter, we provide some methods to find the solutions to both homogeneous and non-homogeneous linear ODEs in a closed form 1 . This is possible only when the given ODE has a particular structure. For instance, one can find a solution in a closed form for any linear homogeneous ODE with constant coefficients whose order is less than or equal to four. After discussing the methods to solve linear ODEs with constant coefficients in detail, we turn our attention toward the linear ODEs with variable coefficients. In particular, we investigate the dimension of the solution space of linear ODEs and study the properties of the Wronskian of the solutions. Moreover, the oscillatory behavior of the solutions to the second order linear ODEs is discussed. Finally, the non-homogeneous linear ODEs are solved explicitly in terms of the the solutions to the corresponding homogeneous ODEs using the method of separation of variables.
