Question

A Non-Constant Coefficient ODE: Solve the non-constant coefficient ordinary differential equation given below:

?2?2???2−34?=0,

subject to the boundary conditions (not initial conditions)

?(0)=0,?(1)=1.

After solving, answer the following questions:

i) Is x = 0 in the ODE

a) an anomalous singular point,

b) an irregular singular point,

c) a regulous singularious point.

d) a regular singular point?

ii) If the coefficient “x2” were replaced with “x3/2” which solution series below would you use?

a) ?=Σ????∞?=0,

b) ?=Σ??+???+?∞?=0, s a constant,

c) ?=Σ??+1??+1∞?=1,

d) ?=Σ????+?∞?=0, s a constant.

Answer 1