@harrysurplus: Replying to @nikayt Here’s how the characteristic polynomial / auxiliary equation comes about. Then there’s three cases of roots to consider :) ✌🏼 ##maths##alevelfurthermaths##alevels##ukschool##teacherpov
I always hated when maths became "let's assume" and you just guess yourself to an answer
2026-07-01 01:35:34
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Bushy :
I assumed this was a skit and was waiting for the gag. Instead I got a quick refresher on DEs, something I've not thought of since uni 20 years ago.
2026-07-02 01:29:14
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Ali Shidhaadh :
Im mad at myself because for some reason I understood what he said 😭
2026-07-02 18:25:42
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nikayt :
yooo that’s me, goated explanation btw, i understood it
2026-07-01 08:10:05
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Joseph :
This is a truely superb video - thank you for such a high quality explanation
2026-06-30 20:01:54
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L O T T I E ꨄ :
Are you actually a maths teacher?
2026-06-30 19:46:38
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Bridled Ape :
Is this considered a rigourous proof for a linear second order constant coefficient homogenous ordinary differential equation???
2026-07-01 07:53:29
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Peach :
where were you October 2025 😭😭
2026-07-02 08:46:45
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shortref :
There is a bit more to this that you'd learn in maths at uni. This guessing gives us two solutions, but doesn't prove that those two are all of them. That depends on the solution space having basis with dimension 2 and showing the two solutions are linearly independent
2026-06-30 23:21:25
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Moonie :
Did I take further maths? no Did i somehow understand what was being said? Yes
2026-06-30 19:47:41
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EmoSupremo :
I feel like I’m back in school and I still have no idea what’s going on
2026-07-01 04:02:15
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Jun Sake :
Holy shit did I really js understand Diffy Qs
2026-07-02 02:15:27
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nicole :
that handwriting is so sexy oml writing out the polynomial
2026-07-01 11:08:08
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kiara!! ⛩️ :
i wouldve loved maths if this guy was my teacher
2026-07-01 11:29:46
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∀𝜁∃𝛾 :
Something that confuses me about differential equations is that if we get two functions that can satisfy the D.E then would they be fundamentally equal? Like if we assumed there was a second function, f(x), that satisfies the D.E s.t. f(x) is not of the form e^(mx), would it be that the outputs of f(x) would be exactly equal to e^(ax) given that their initial values are the same?
2026-07-01 05:00:17
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Nathan :
I did btec engineering and did calculus actually understood what went on
2026-06-30 22:03:32
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ToastedMathℤ :
Oh learning this is going to be so fun
2026-07-01 06:00:48
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MmFb414042 :
Even better: what we actually do is to factorize the equation by viewing d/dx as an operator. Have a d^2y/dx^2 + b dy/dx + cy = a(d^2/dx^2 + b/a d/dx + c/a)y = a((d/dx + b/(2a))^2 - b^2/(4a) + c)y = a(d/dx - (-b + √(b^2 - 4ac))/(2a))(d/dx - (-b - √(b^2 - 4ac))/(2a)). I.e to factorize the equation you treat it as a polynomial and solve for the roots. So with roots λ1 and λ2, we have (d/dx - λ1)(d/dx - λ2)y = 0. Subbing u = (d/dx - λ2)y, the above gives (d/dx - λ1)u = 0, so u = A exp(λ1x) + B = (d/dx - λ2)y = exp(-λ2x) d/dx(exp(λ2)y), so y = A exp(λ1x) + B exp(λ2x) + C with λ1 and λ2 the roots
2026-07-01 15:20:56
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FUNBOY :
i like this,you're a good math teacher
2026-07-02 04:07:04
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merlincontroltower :
Very well explained!
2026-07-02 03:11:22
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Das Raffnix :
What does this have to do with Anzacs?
2026-07-02 15:08:09
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Shaz1994 :
So everything is equal to zero because there are no numbers. No numbers yet everything is equal to zero. How will this help us in real life?
2026-07-01 15:48:23
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ABK :
Amazing video mate. Just a little mistake you made when going over the substitution; instead of saying the first derivative you said the second derivative when substituting the variable for b the first time, although the mentioned the correct one the second time you went over. You'd probably want a pop up on the video saying "first" for the people that are learning this and might get confused
2026-07-01 20:20:35
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International :
Great. Part 2.
2026-07-01 10:40:31
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