Consider the partial differential equation ux−ut=0. Trying to solve this differential equation with the method of separation of variables, we assume that there is a product solution for this equation of the form u=XT such that X=X(x) and T=T(t). From the options below, select ALL the correct statements. The solution for the first order separable ODE corresponding to T will be T=be−λt The solution for the first order separable ODE corresponding to X will be X=ce−λx The product solution for the given PDE will be u=ke−λ(x−t). After rewriting the equation in terms of X and T, I will divide both sides of my new equation by xtXT. The solution for the first order separable ODE corresponding to X will be X=e−λcx The solution for the first order separable ODE corresponding to T will be T=beλt After rewriting the equation in terms of X and T, I will divide both sides of my new equation by XT. The product solution for the given PDE will be u=ke−λ(x+t).
