x = 0 is an ordinary point of a certain linear differential equation. After the assumed
Chapter 5, Problem 4(choose chapter or problem)
x = 0 is an ordinary point of a certain linear differential equation. After the assumed solution y = L::= 0 cnx n is substituted into the DE, the following algebraic system is obtained by equating the coefficients of x 0 , x 1 , x2, and x 3 to zero: 2c2 + 2c1 + c0 = 0 6c3 + 4c 2 + c1 = 0 12c4 + 6c3 + c 2 - lei = 0 20c5 + 8c4 + c3 - k1 = 0. Bearing in mind that c0 and c1 are arbitrary, write down the first five terms of two power series solutions of the differential equation.
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