How to handle duplication in method of undetermined coefficients

[@RadicalRacoon]

awesome video! Thank you

[@에반-d3q]

Thanks for the great lecture. I am not sure why (Ax)(e^3x) + 4Be^4x does not work. Could you please explain it in detail

[@jhondelion8044]

Why is there positive on Yp?

[@daniel_an]

The coefficients A and B could be negative, so there is no need to have it as negative. You could put the minus if you want, but you may get confused what to do after getting A and B.

[@DondoGaming]

What if duplicates happen within yp? (any response is greatly appreciated!)

[@daniel_an]

It's hard to explain here. If you have x e^x and e^x in the right hand side, then you put both in yp. But if e^x is one of the complementary solutions, then you have to bump up the powers and write x^2 e^x and x e^x.

[@DondoGaming]

@@daniel_an thanks! For context, this is where I got that situation: y''-4y'+4y = (x^3)(e^(2x)) +x*e^(2x) This is pretty tricky to do in my case. Yc is pretty easy to get, but what about Yp here? (As always, any response is greatly appreciated)

[@daniel_an]

@@DondoGaming (Ax^3+Bx^2+Cx+d)x^2 e^2x

[@DondoGaming]

@@daniel_an i see. So you combined some terms into one? (With regards to Yp)

[@srihartono6824]

@@daniel_an I thought you forgot something , it should be (Ax^4+Bx^3+Cx^2+Dx+E)x^2. e^2x