I just tried using Laplace transforms but i get a slightly different solution. Almost the same. What method did you use?
characteristic equation of second grade ordinary diff eq. and then parameter variation method... that's the way i think is done
that's cheating lol i know it'd work but u gotta get the solution by solving the diff eq... what if you didn't have the answer........
well i got the answer few days ago, been busy lately but for the record im gonna post the answer..as usual if im wrong correct me plz...
so i got the general solution
so
remember that
then the general solution is:
now i gotta get the particular solution which i got with parameters variation method...
so:
where and are unknown but according to the formula:
;
where
and
then
so
and the particular solution is:
and finally
now the initial values:
so
so
then the solution for the initial values is: