Stuck on the following problem, unsure of how to go around it
1a.
For what none values of k does the function
satisfy the differential equation
1b.
for those values of k, show that every member of the family of functions
(where A and B are constants) is also a solution to the differential equation.
1c.
come up with a second order differntial equation for which
is a solution for the same values of k obtained in part (a)
im usually ok with differentail equations but unsure when it comes to the worded versions
for 1a i tryed the following but werent sure where else to go
so one possible solution is k = +/- 5 but im not sure if that is the right thing to do
Any help is most appreciated