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