Should this actually be
?
If so...
You plan to make the substitutions and .
This would mean .
It would also mean
and
.
So finally we can substitute into the original DE...
.
You should be able to solve this now...
Hello!
I having problems getting started with this problem:
Using subn and rewrite:
hence find all solutions.
When I perform the substitution using and , I get:
I can't find any complimentary functions and probably due to my undergrad engineering major, I tried a Laplace transform, but end up with a horrible function owing to the part that would leave a on the LHS- I suspect this is not be the correct method as alluded to within the question - there must be a reason for the subn.....
I can't use an order reduction or variation of parameters as I don't have an already known solution- unless I use a trial and error! If anyone can kick me in the right direction, I will be most greatful.... I can't seem to see through it right now!
Thanks for looking!
Should this actually be
?
If so...
You plan to make the substitutions and .
This would mean .
It would also mean
and
.
So finally we can substitute into the original DE...
.
You should be able to solve this now...
I am getting to a difficult integral on the
The aux eqn is
giving roots of and giving compliemntary function:
Evaluating the wronskian determinents:
which drops to be
this leaves
and similarly for with replaced by
It does not seem to possible to integrate .... have I made an error in my working or gone off track somewhere?