Answer Happy

5. If the coefficients in a second-order linear ODE have a regular singular point at x = a, the method of Frobenius suggests a power series solution as y = Enzo An (x – a)n+r, where the coefficients and "r" are to be determined via substitution of the series into the equation, and from the boundary conditions. Which statement is correct? a) there are only two options, 11 = 2 and 12 = -2 b) all indicial equations are the same, and have the same roots c) the roots n and r2 of each indicial equation for different powers of x are not the same, but the general solution is the same d) the roots r; and r2 of each indicial equation for different powers of x are not the same, and therefore there are many different general solutions for the ODE e) if x=a is a singular point, there is no solution