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STEP III 1997 question 6 solution
From The Student RoomTSR Wiki > Study Help > Subjects and Revision > Mathematics > STEP > STEP III 1997 question 6 solution Solution 1If So So This has general solution
To use the 2nd boundary condition, observe
So
But Solution by DFranklin Solution 2(1) Differentiate (1) to get (2):
Substitute (1), (2) and The general solution of this linear homogeneous second order differential equation is We have
It follows that
Upon expanding with Trigonometric Addition Formulas and adding
Solution by khaixiang |










then
.
as desired.
.
.
and so we have:
and so
.
(which is also
). Finally, we need to show:
.
, hence result.
into
to get
We are given y(1)=1, hence after the tranformation of
which really means that
is an even function when n is either 0 or even. And that it's an odd function when n is odd. But after the substitution of
becomes an even function for all n since cosine is an even function.
which can only be even for all n when B=0
and
for
and
as required.
and
:
as shown.





