Next: Extending the result
Up: Deducing
Previous: Differential equation for
Since we know that is a polynomial of degree , we can put

(4) 
and it follows that
Substituting these into (3) gives
Comparing coefficients of on both sides, we find and

(5) 
(for
).
Using (5), we obtain
There is a clear pattern emerging and we can make the conjecture

(6) 
To prove (6), we note that
It follows that (6) is correct, by induction.
To find we simply substitute into (6) and
immediately obtain
Substituting into (4), we obtain the^{1} polynomial solution to
(3),
Next: Extending the result
Up: Deducing
Previous: Differential equation for
Alexander Frolkin
20010602