5. [9 marks] The reaction H in happiness units by a consumer receiving Y units of a product can be modeled by the differential equation, dH dy k Y + 1 where k is a positive constant. (a) Solve the above equation for H. (b) Re-write the solution in terms of the initial condition H(0) = 0. (c) Assuming k = 1, write an Euler scheme and compute until the number of units received is 25 (using Excel, Matlab, Octave or similar). (d) Plot both of your solutions on the same set of axes and comment on the appropriateness of each method used in part (a) and (c).