Consider the partial differential equation ∂2f/∂x2 + ∂2f/∂y2 = 0, where x, y are real. If f(x, y) = a(x)b(y), where a(x) and b(y) are real functions, which one...

u(x, y) is governed by the following equation: ∂2u/∂x2 - 4(∂2u/∂x∂y) + 6(∂2u/∂y2) = x + 2y. The nature of this equation is: _______.

Let u(x,t) denote the displacement of a point on a rod. The displacement satisfies the following equation of motion:∂2u/∂t2-25∂2u/∂x2=0 , 0