  It is well-known that any solution of the Laplace equation is a real or
imaginary part of a complex holomorphic function. In this paper, in some sense,
we extend this property into four order hyperbolic and elliptic type PDEs. To
be more specific, the extension is for a $c$-biwave PDE with constant
coefficients, and we show that the components of a differentiable function on
the associated hypercomplex algebras provide solutions for the equation.
