Differential Equations

D'Alembert's general solution to the one-dimensional wave equation $u_{tt} = c^2 u_{xx}$ is expressed as:

Options:

• (A) $u(x, t) = f(x - c t) + g(x + c t)$
• (B) $u(x, t) = f(x) g(t)$
• (C) $u(x, t) = e^{-c t} \sin x$
• (D) $u(x, t) = f(x - c t) g(x + c t)$