x2 − a2t2 t

This equation is also known as the equation of vibration of a string. The wave equation is often encountered in elasticity, aerodynamics, acoustics, and electrodynamics. 2.1-1. General solution. Some formulas. 1◦. General solution: w(x, t) = ϕ(x + at) + ψ(x − at), where ϕ(x) and ψ(x) are arbitrary functions. 2◦. If w(x, t) is a solution of the wave equation, then the functions w1 = Aw(±λx + C1,±λt + C2) + B, w2 = Aw x − vt