F(x) = x^2+3x-4 and g(x)=x-1
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The general form of the geometric sequence is 
, where a sub n is the number term you're looking for (we're looking for the tenth term). a sub 1 is the first term in the sequence (ours is -6), r is the common ratio, and n-1 is the numbered term you're looking for minus 1. Our formula then looks like this: 
. Simplify it to 
. Take 2 to the 9th power then multiply it by -6 to get -3072. C is your answer.
Let . Then
and substituting these into the ODE gives
Let , so that
. Then the ODE is linear in
, with
Multiply both sides by , so that the left side can be condensed as the derivative of a product:
Integrating both sides and solving for gives
Integrate again to solve for :
and finally, solve for by multiplying both sides by
:
already accounts for the
term in this solution, so the other independent solution is
.