2. Suppose that particles move only by diffusion. Suppose that a number No of particles are injected at x = 0 at time t 0, and another Ni particles are injected at r = 0 at time t1 > 0. a) Write down the function N(x, t) that gives the density of particles at location x at time t. Hint: The PDE is linear so you can add solutions. Note that you will have different formulas for 0 t b)Let1 and use a computer program (R, Matlab, Mathematica, Maple, etc.) to plot the solution at x = 1 as a function of time for diffusion coefficients D = 10-3 and D = 10-6 Comment on the concentrations you obtain 2. Suppose that particles move only by diffusion. Suppose that a number No of particles are injected at x = 0 at time t 0, and another Ni particles are injected at r = 0 at time t1 > 0. a) Write down the function N(x, t) that gives the density of particles at location x at time t. Hint: The PDE is linear so you can add solutions. Note that you will have different formulas for 0 t b)Let1 and use a computer program (R, Matlab, Mathematica, Maple, etc.) to plot the solution at x = 1 as a function of time for diffusion coefficients D = 10-3 and D = 10-6 Comment on the concentrations you obtain