Hi there,
I have a question that states:
Obtain the general solution of by factorizing L into two first order linear operators.
My thoughts on what to do, is it divide through by t, then make = y, = y' and = y''.
That makes . Then solve for this first order DE. Once finding a solution to that DE, replace y'' with the answer, than solve the first order linear equation then.
I was wondering whether my thought process was right. Is my method correct?
Thanks for your time.
I messed up interpreting the differential operators and mistakenly treated them as algebraic. So I'd like to start over please.
We have or and I want to find a product of two linear operators of the form:
Therefore:
and by inspection and a little messin' around, I get: and so I can now write the DE as:
and therefore we can solve: