Assuming that the equation (l - x)y\" + xy\' - 2y = 0 has a power series solutio
ID: 3081942 • Letter: A
Question
Assuming that the equation (l - x)y" + xy' - 2y = 0 has a power series solution of the form Y = find the recurrence relation among the coefficients that is induced by the differential equation. an + 2(n + 1)n +an + 1(n + 2)(n + 1) + an (n- 2) = 0 an + 2(n + 1)n-an + 1(n + 2)(n + l)+an(n - 2) = 0 an + 2(n + 1)n + an + l(n + 1)n + an(n - 2) = 0 an + 2(n + 1)n - an + 1 (n + 1)n + an(n - 2 ) = 0 an+2(n + 2)(n + 1)+ an + 1(n + 2)(n + 1)+ an(n - 2) = 0 an + 2(n + 2)(n + l) -an+ 1(n + 2)(n + 1 ) + an(n - 2) = 0 an + 2(n + 2)(n + 1)+ an + 1(n + 1 )n + an(n - 2) = 0 an+2(n + 2)(n + 1)- an + 1 (n + l)n + an(n-2) = 0Explanation / Answer
we see for the coefficient of x^n in lhs...and equate it to 0...coeffn of x^n in LHS is (n+2)(n+1)an+2 -(n+1)nan+1 +n*an - 2an =0 ...or (n+2)(n+1)an -n(n+1)an+1 +(n-2)an =0 ...hence the ans is (h) ...feel free to ask doubts please rate n reward .. :)