The equation (d2^u/dt^2) - (delta u) = 0 is classified as a hyperbolic equation due to its structure resembling the hyperbolic equation x^2 - y^2 = 1. Hyperbolic equations, such as the partial differential equation ∂²u/∂t² = ∂²u/∂x², exhibit two characteristic lines that aid in their solution. This contrasts with parabolic equations, like the heat equation, which have only one characteristic line, and elliptic equations, such as Laplace's equation, which lack characteristic lines altogether. The classification of these equations is essential for understanding their behavior and solving them effectively. Understanding hyperbolic equations is crucial in various fields, including physics and engineering.