D'Alembert formula
= D'Alembert formula
{c}
{wiki=D'Alembert's_formula}
The Cauchy problem $u_{tt}=c^2u_{xx}$ has
$$
u(x,t)=\frac{f(x-ct)+f(x+ct)}2+\frac1{2c}\int_{x-ct}^{x+ct}g(y)dy.
$$
= D'Alembert formula
{c}
{wiki=D'Alembert's_formula}
The Cauchy problem $u_{tt}=c^2u_{xx}$ has
$$
u(x,t)=\frac{f(x-ct)+f(x+ct)}2+\frac1{2c}\int_{x-ct}^{x+ct}g(y)dy.
$$