How can i convert nonhomogeneous ode to homogeneous ? I have an equation system
$$y'(t) = M(t)y(t)+h(t)$$ 
where $[M(t)]_{2\times2}$ square matrix  and  $[h(t)]_{2 \times1}$ is the nonhomogeneous part of the system. I can solve numerically homogeneous systems as $y'(t)=M(t)y(t)$ with my algorithm which is in my topic(Is it true for solving differential equations by getting constant coefficient matrix with magnus expansion) but for nonhomogeneous one I am not sure how can i do it. 
In this paper (http://personales.upv.es/serblaza/2012APNUMdoi.pdf) equation(17-18), I found  some useful informations about numerical solutions of nonhomogeneous systems but, i'm still suspicious solving nonhomogeneous systems with my algorithm.
Is there any way converting nonhomogeneous systems to homogeneous systems for solving numerically as above type equations ? 

You can transform the system into a homogeneous one by adding an additional constant component $y_{n+1}\equiv 1$ so that 
$$
\pmatrix{\dot y_{1:n}(t)\\\dot y_{n+1}(t)}
=
\pmatrix{M(t)&h(t)\\0&0}
\pmatrix{y_{1:n}(t)\\y_{n+1}(t)}
$$
with $y_{n+1}(t_0)=1$.
