6 pairs of sock for $6.99. 10 pairs of socks for 11.99. which is the better buy
2 answers:
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The solution depends on the value of 
. To make things simple, assume 
. The homogeneous part of the equation is
and has characteristic equation
which admits the characteristic solution
.
For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be
. Then
So you have
This means
and so the general solution would be
and has characteristic equation
which admits the characteristic solution
For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be
So you have
This means
and so the general solution would be