Differential Equations | A higher order non-homogeneous differential equation.

We present a solution to a higher order non-homogeneous differential equation. This problem was suggested by subscriber
SiggiTheHopper2.

[davidblauyoutube]

Great exposition!
Personally, I would have used operator algebra, noting the operator equation (e^-rx)D = (d/dx)e^-rx. This equation can be shown very quickly by using a test function. Then the initial equation can be written 1 = e^(-rx) D^N y = (d/dx)^N (e^-rx y). Direct integration N times of both sides yields x^N/N! + (arbitrary deg N-1 polynomial) = e^-rx y, from which the solution is immediate.

[FreemonSandlewould]

I like this guy. "Great so that's the end of the video" Fun watch and good execution of the explanation.

[bigjazbo]

At 6:15 you wrote k+1 choose n, but you meant k choose n+1.

[billclintonscomputer]

what branch of math is this? Cause I dont get a thing haha

[FunctionalIntegral]

But you are guessing the solution for y at 6:50 on which you apply the Lemma from the beginning. This is not a satisfactory way of solving DE, and far from a systematic treatment of DE.