Problems On Frobenius Series Solution

Problems on Frobenius Series Solution-1:

Example 2: This time a formula for the solution was not found bt the computer algebra software. so I will settle for a more modest task: Find the first threeterms of Forbenius solution around x = 0 for

Solution: For eaiser handling of the series, write

and we take only the first three terms:

Since a₀ ≠ 0, actually we can take a₀ = 1, larger of the integer value of r is r = 1.

Example 3: Consider the different equation

Which has solution y = A / (1-x). By the series method we would obtain;

Multiply out by the -x factor and taking it over to the other side.

Now change the dummy index on the left by letting n → n 1, to give

The indicial equation is obtain by demanding that the lower power, corresponding that the lowest power, corresponding to n = -1 on the left hand side, should vanish. This requires k = 0. The recurrence relation is then.

    a_{n 1} = a_n

Full Solution is: