After verifying that the power series method applies, find the general solution (to 5 terms) using the power series method to the DE: + 4 + 10y = 0. Guess solution: y = a0 + al*x+ a2*x^2 + a3*x^3+ a4*x^4 + . y'= * . (up to z term) y" = * . (up to z? term) Find recurrence relations (in terms of a0 and a1) by equating the coefficients of z", for n=0,1,2,. az az = a4 Find the general solution to 5 terms (i.e. to x^4 term) in terms of a0 and al: y = ao( +...) + a1( +...)

A) The fraction  b/a  may be written as  b/a = (a+b−a) / a = 1 + (( b−a ) / a ). Use the power series expansion  ln(1+z)= z + z^(2) / 2+ ⋯) , valid for  |z|<1 , to find approximate expression for the inductance when  b−a  is much less than a. Express your answer in terms of the variables  N ,  I ,  h ,  b ,  a , and appropriate constants. L = ? B) Compare results with this L = μ0*N^(2)*A / 2πr .

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Express the function as a power series by first using partial fractions. 2x + 6 x2 + 6x + 5 f(x)= ㅇ 화-10+ n = 0 n = 0 0 -1)"| (-1)7x2 n = 0 퇴 ∑|1 n =0\ 1 2²+1 퇴 n=0 5n+1 1 52+1 1 52+1