Question

3. Find the minimum radius of convergence for the power series solution y= Ê cox" of the ODE: n=0

Answer 1

So 2 n=0 expressed in terms of both to and C. Find the minimum radius ob convergence for the power series solution y = 2 Copth of the ODE You 15% question is incomplete because differential equation does not mention in question lot Take an example. If we seek a power series solution for the differential equation Y" - (l+cy= Во we obtain Co-flo and three term recurrence relacion CR+2= CK + CR- a Kal,2,3, CK+1) (K+2) gt follows from these two resultes that all coefficientes en for n=3 are we can flast choose Coto, C, = 0 this yields Coeffluenter for one Solution esepdelsed entirely in terms of co! -6, CScanned with CamScanner

using 1 for the other solucion are Next , ib. we choose Co-o, C, to, then Coeffiuente expressed in terms of C,- both cases, the C - 16 in recusante relation for k= 1, 2, 3 .. gives Co to a C - 0 co (z = Citco= Cole 2-3 at Co eff - Catci - Co 3.4 2.3.4 Co Czt(g =co 4.5 4.5 L Co 30 6 ☺ Co=0, C, zo (g = 160=0 Citco L = C 2.3 6 Cu Cote & C = 1 3.4 3.4 Czt a Colla G 4.5 4.5.6 120 CScanned with CamScanner

Finally equatich general solution of the y- coyoc) + (, ya (x) y, GC) - It fol + L + x + 1 ore 4 5 - and + L x + Ya (x) = x+ Lo + 1x + Each Series Converges values of x for all finite think this this example will help you because your question is not complete CScanned with CamScanner