l. [Pts4] Here is a version of the Worrnersley equation for blood ow where p is density and p. is viscosity and worn} = wztr1t} is the longitudinal velocity {along the axis) as a function of r, the distance from the center ofthe artery and time. t. The pressure gradient takes the form 2P- AEi'\" and the boundary conditions are a 3i =o. w[a) =o r-tll' r-[l Substitute for gy- above and solve for wtr,t} in the equation above by separation of I m and let v = E. Find the differential equation for u{r] p variables. Take wfr,l} = ufrle and solve it (see hints]! Hint: Solutions to the resulting equation involve both a homogenous and particular solution. The particular solution is \"particularly" easy to guess think constant with respect to r. The homogenous solution requires that you make a variable substitution to get it into the form of a Bessel equation it's almost obvious what it has to be. Do it! You will now have a general solution to this equation that is a superposition of Bessel functions of the first and second kind. Finally applying the boundary conditions, along with looking at plots of the Bessel functions of the second kind will point you to the solution in the paper, {equation 8] in terms of only Bessel functions of the rst kind. Write your solution in terms of alpha {defined in paper] and the variable y. Compare your solution to equation 9 in the paper. If we also write r/R=y, then the velocity is given by A1 Jolayit w= + 1- eint. p in Jolait)