The Form of the Particular Solution Using the Method of Undetermined Coefficients - Part 1

This video provides examples of how to determine the form of the particular solution to a linear second order nonhomogeneous differential equation. The particular solution is not found.

[Mathispoweru]

The problem states to assume no terms in y_p are duplicates of y_c since we don't know y_c.  As a result, not extra factor of x is needed.   

[mattklinger]

Thanks for the videos. Finding Yp really got me hung up on this topic so this is like a light in the darkness lol. I find that I prefer to form Yp for every term regardless if I can make it in to a "quadratic" function or something similar to save steps because it makes more sense to me. Then I group all my coefficients and reduce any coefficients being added on the same term to one coefficient like you did in the first problem.

[kongmunky]

Hi thanks for posting these up. Great help.

I have a question: In your first example (A+D)sin(3x) becomes Esin(3x). Shouldn't it become Exsin(3x) as I watched in your later videos that if there is a repeat u add a "x"

[sfaulder]

great video- but isn't the derivative of cos negative sin? so it would be Ccos(3x)-Dsin(3x)...?

[mkusasakala]

Thank you very much sir! your explanations are very clear!

[username]

It is probably too late but:
We would want an x in there only if there was sin(3x) in the y.c term (which you get by solving the homogeneous part). In the first example we don't know the y.c term so we don't know if the extra x is necessary or not.

[Jamillakitchen]

where is the The Form of the Particular Solution Using the Method of determined Coefficients series?

[adelsaade]

and how to find A B C D when substituting in the 2nd degree ODE??

[TheCudi]

this is wrong you need to add an X to make the e^-x particular