(a) To determine the radius of convergence of the series solution in Example, write the sc...

(a) To determine the radius of convergence of the series solution in Example, write the scries of terms of even degree in Eq in the form

where an = c2n and z = x2. Then apply the recurrence relation in Eq and Theorem to show that the radius of convergence of the series in z is 4. Hence the radius of convergence of the series in x is 2. How does this corroborate Theorem in this section? (b) Write the series of terms of odd degree in Eq in Lhe form

to show similarly that its radius of convergence (as a power series in x) is also 2.