  Most results on quaternion-valued differential equation (QDE) are based on J.
Campos and J. Mawhin's fundamental solution of exponential form for the
homogeneous linear equation, but their result requires a commutativity
property. In this paper we discuss with two problems: What quaternion function
satisfies the commutativity property? Without the commutativity property, what
can we do for the homogeneous equation? We prove that the commutativity
property actually requires quaternionic functions to be complex-like functions.
Without the commutativity property, we reduce the initial value problem of the
homogeneous equation to a real nonautonomous nonlinear differential equation.
