A-Level Further Maths I4-05 2nd Order Differential Equations: Repeated Roots

[two]

This whole time I've been using the auxiliary equations without knowing WHY they worked. This video was very insightful.thanks!

[dillonlamb]

Very Helpful! I've just started a physics degree and half of of the class has already done further maths, and half (including myself) haven't

[scollyer.tuition]

Very nice motivational approach to the repeated root question, which is all too often presented as a Deus-ex-machina solution.

One point that I might have mentioned: all homogeneous linear 2nd order DEs can be shown to have 2 (linearly independent) solutions, and a linear combination of the two solutions is the general solution. Here, we can show that the functions { e^{4x}, xe^{4x} } are solutions of the original DE by direct substitution, so their l.c. is the general solution.

[Mugen-]

hello, at 5:43, should it be (a+bx)e^4x since they have the same root? or does it not matter at all?