Consider the following differential equation. (1+7x²)y"-6xy-24y = 0 (a) If you were to look for a power series solution about xo -0, i.e., of the form Σ 11-0 then the recurrence formula for the coefficients would be given by ck+2 g(k) into the answer box below. = g(k) ck, k≥2. Enter the fu (b) Find the solution to the above differential equation with initial conditions y(0) = 0 and y'(0) = 8. (Note that this solution is a terminating power series.) (c) Find the first three nonzero terms in the solution to the above differential equation with initial con y(0) 5 and y'(0) = 0.