to find all 
such that 
.Using the formula,
A product of numbers is equal to zero only if one of the factors is zero, so either 
or 
.
Now we have two different linear equations to solve.
when 
or when 
.
So we get particular solutions 
or 
.
We get all solutions by adding multiples of the period, which is 
, so the solutions for this linear equation are of the form:
The other possibility was 
.
We get particular solutions 
and 
.
We get all solutions by adding multoples of the period, 
, to these.
So all solutions are of the form
Now put all these together. Solutions to 
are all of the form:
or
So we need to solve
We have a quadratic equation in 
.
Move everything to one side of the equation and use the quadratic formula.
Now we have two different linear equations to solve:
However, one of these equations is impossible. The range of 
is 
, but 
, so 
.
So the only possible solutions are solutions of
Solutions to 
are all of the form:
These are also the solutions of 
to find all solutions of 
The two particular solutions are 
and 
.
The general solution is
Date: 2008/11/11 19:02:02