Each of these ODEs is linear and homogeneous with constant coefficients, so we only need to find the roots to their respective characteristic equations.
(a) The characteristic equation for
is
which arises from the ansatz 
.
The characteristic roots are 
and 
. Then the general solution is
where 
are arbitrary constants.
(b) The characteristic equation here is
with a root at 
of multiplicity 2. Then the general solution is
(c) The characteristic equation is
with roots at 
, where 
. Then the general solution is
Recall Euler's identity,
Then we can rewrite the solution as
or even more simply as
The draw back would be that many crimes would go unpunished. Some victims could be to scared, some would prefer to forget about the crime and focus on other things in their lives.
Here are some points that could be used :
1. seceding would reduce the amount of resource that the nation as a whole had, so the federal government shall not allowed it to happen.
2. Many people in the population might not agree to the secession so the government had to protect their interest,
3. Secession make our nation become much more vulnerable to attacks, since foreign nations can leverage the separation to gain allied that close to us.
Well, I don't think you can present any evidence to show she is wrong. Behaviorists believe that children and any human being acquire language through conditioning - you present them with a condition under which they learn a certain language. Since this woman is a behaviorist, I don't see why she is wrong in believing what she does.
