Find the general solution of the second-order differential equation
where for
, and
for all other
.
If or
, then we have the equation
This is of the form with
and
. Therefore,
so the solutions are given by
If , then we have the equation
A particular solution to this equation is given by (since
in this case). Therefore, all solutions are of the form
Would it be possible to turn this into piecewise solutions for all x by looking at the values of y(1) and y(2) IN EACH CASE?
in each case* – did all caps on accident 0_0