Let k, b be constants where k > 0. Let v(x, t) be the solution to the following nonlinear diffusion equation vt(x, t) - kver(x, t) + blur(x, t)]' =0 (-00 0) with initial condition v(r, 0) = x. (1) Let u(r, t) = e Ev(z,t) Show that u(x, t) is the solution to the diffusion equation ut(x, t) - kurr(x, t) = 0 (-00 0) with initial condition u(x, 0) = e-#x (2) Find the formula for u(r, t). (3) Find the formula for v(r, t). Notes: The transformation from v to u is called the Cole-Hopf transformation