Discussion
Consider a function u which depends on position x and time t. The partial differential equation
\(\dfrac{\partial u}{\partial t}=\dfrac{\partial^2 u}{\partial x^2}\)
is known as the
Answer: B
It is the heat equation.
The one-dimensional heat (diffusion) equation is \(u_t=\alpha\,u_{xx}\) (subscripts denoting partial derivatives): the first time derivative equals a constant times the second space derivative. Here the constant is 1.
The wave equation has the second time derivative, \(u_{tt}=c^2u_{xx}\). Laplace's equation has no time derivative at all, \(\nabla^{2}u = 0\). There is no standard 'elasticity equation' of this form.
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