Consider the differential equation 1 x2y 4xy 6y 0 Give re

Consider the differential equation (1 + x^2)y\" -4xy\' + 6y = 0 Give reasons as to why 0 is an ordinary point of that ODE. One of the first step in solving this differential using power series would be to obtain a recursion formula. Determine the recursion formula. Solve this recursion formula to obtain the general solution of this differential equation. What particular solution do we obtain if we have y(0) = -3 and y\' (0) = 1?

Solution

Recursive Formula

For a sequence a₁, a₂, a₃, . . . , a_n, . . . a recursive formula is a formula that requires the computation of all previous terms in order to find the value of a_n .

Recursive Formula For a sequence a1, a2, a3, . . . , an, . . . a recursive formula is a formula that requires the computation of all previous terms in order to find the value of an .