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We consider exponential integrators based on the Magnus series expansion for the numerical integration of general linear non-homogeneous differential equations. The schemes can be considered as averaged methods which transform, for one time step, a non-autonomous problem into an autonomous one whose flows agree up to a given order of accuracy at the end of the time step. The problem is reformulated as a particular case of a matrix Riccati differential equation and the Möbius transformation is considered, leading to an homogeneous linear problem. The methods proposed can be used both for initial value problems (IVPs) as well as for two point boundary value problems (BVPs). In addition, they allow to use different approximations for different parts of the equation, e.g. the homogeneous and non-homogeneous parts, or to use adaptive time steps. The particular case of separated boundary conditions using the imbedding formulation is also considered. This formulation allows to transform an stiff and badly conditioned BVP into a set of IVPs which can be integrated using some of the previous methods. The performance of the methods is illustrated on some numerical examples.

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