Hey I need to solve this problem by means of inverse operators:

Thank you!Quote:

y''-3y'+2y=x

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- Dec 5th 2010, 06:52 PMdeltafeeInverse operators
Hey I need to solve this problem by means of inverse operators:

Thank you!Quote:

y''-3y'+2y=x

- Dec 6th 2010, 08:05 PMTheEmptySet
Just FYI your questions are very vague.

I think this is what you mean...

Solving for y gives

Since is a polynomial we can express each operator as a geometric series, but 1st partial fractions gives

Then

and

Combing the sums gives

Note that since the right hand side is only a degree 1 polynomial we only need two terms from the series

So this gives

You still need to use the eigenfunctions to find the complimentary solution. - Dec 7th 2010, 02:44 AMAckbeet
Very elegant!