Determine the form of a particular solution, second order linear differential equation, sect4.4 #29

Form of a particular solution with undetermined coefficients,
particular solution for a non-homogeneous differential equation,
second order non-homogeneous linear differential equations,

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[kierancalder]

better that kahn academy in this topic, my everlasting pain has been transformed into a rainbow of opportunity. THANK YOU!

[DougCube]

Solving for the constants, you should get A=5/56, B=0, C=0, D=0, E=0, F=0, G=0. So y_p is simply (5/56)(t^8)e^(3t). Plugging this solution in to the original, does indeed check out.

[sergiorome]

thank you so much much more clear than my textbook

[khemrajchaulagai]

thank you so much for your wonderful lecture sir .

[samwanyoike]

what if it was just t(e^t) whay will the particular become

[FyahJourney]

Why do you put 't' before C2 * E^(3t) when you don't for C1? More explanation wanted.

[dujas]

There is a much easier method to solve this problem. Substitute u=y'-3y and the left side becomes u'-3u. In fact, if you multiply both sides by e^(-3t) from the start, the left side becomes simply (e^(-3t)y)'' and the right hand side is just a polynomial. Just integrate both sides twice and multiply by e^(3t)

[HC-gr]

excuse me, but why you did NOT multiply by A for the sake of e^3t ?, I hope that makes sense.
I mean we usually multiply by A for constant which is follow e^3t

[yuganeswarman]

I think for this, Method of Variation Parameter is more suitable

[mathadventuress]

how in the heck do i have the same book?!?!?!?