# Tips when finding particular solution to a 2nd order ODE

• September 17th 2010, 10:31 PM
acevipa
Tips when finding particular solution to a 2nd order ODE
Does anyone have any quick way of finding the particular solution to a 2nd order ODE?

I know what to guess, but my textbook is saying that if the guess for the particular solution is "a solution to the homogenous ODE", then multiply by x? Is there are way to avoid this step.
• September 17th 2010, 10:44 PM
Prove It
Quote:

Originally Posted by acevipa
Does anyone have any quick way of finding the particular solution to a 2nd order ODE?

I know what to guess, but my textbook is saying that if the guess for the particular solution is "a solution to the homogenous ODE", then multiply by x? Is there are way to avoid this step.

No there's not a way to avoid this step. If you don't multiply your guess by $x$, then when you substitute your function and its derivatives into the DE, you won't be able to evaluate the coefficients.