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
For a given c1 and c2, aren’t there additional constraints on a and b?
For the derivative of y at x = 1 and x= 2 to exist, y needs to be continuous at those points.
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