Boundary Value Problem via Separation of Variables
Consider the differential equation \(\frac{dy}{dx} = ky\) where \(k\) is a constant. Given the boundary conditions \(y(0)=A\) and \(y(L)=B\) with \(A \neq 0\) and \(B \neq 0\), separate the variables and solve for the constant \(k\) in terms of \(A\), \(B\), and \(L\).