HARDEST 25 Mark Second Order Differential Equation Question EVER | A Level Further Maths
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- Опубликовано: 5 фев 2025
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this is the usual stuff that we got taught but the annoying thing is that is so long to complete it, amazing video btw!
deepseek R1 is kinda goated i asked it to solve it without the show that part, i just told it to find x(t) and it found the answer in 99 seconds, as it says in the question
i also asked it for exam strats for this kind of question.
Under exam conditions, several aspects of this problem could pose significant challenges:
Recognizing Resonance in the Particular Solution
The nonhomogeneous term 4e^-t (cos2t + sin2t) overlaps with the homogeneous solution e^-t (C1 cos2t + C2 sin2t). Identifying that the particular solution must be multiplied by t (due to resonance) is critical. Missing this step leads to an incorrect guess for x_p(t), causing the solution to fail.
Tedious Derivative Calculations
Computing derivatives of x_p(t) = t e^-t (A cos2t + B sin2t) involves lengthy product rule applications. For example:
x_p' = e^-t [(A - At + 2Bt) cos2t + (B - Bt - 2At) sin2t]
Sign errors or coefficient mistakes are highly likely under time pressure.
Matching Coefficients for A and B
Substituting x_p into the differential equation gives the system:
-4A + 4B = 4 (from cos2t)
-4B - 4A = 4 (from sin2t)
Solving this requires careful algebra-arithmetic errors propagate into the final answer.
Applying Initial Conditions
The general solution combines terms:
x(t) = e^-t [(C1 - t) cos2t + (C2 + t) sin2t]
Applying x(0) = 1 gives C1 = 1, but differentiating terms like -t e^-t cos2t for x’(0) = 2 is error-prone under stress.
Time Pressure and Stress
Multiple high-stakes steps (resonance, derivatives, algebra, initial conditions) must be executed flawlessly. Mistakes at any stage invalidate subsequent work.
Key Takeaways for Exam Success:
🔄 Practice resonance cases (overlapping homogeneous/nonhomogeneous terms).
📝 Streamline derivatives (use tabular integration/mnemonics).
✔ Double-check algebra (verify coefficients and substitutions).
🗂 Stay organized (track homogeneous/particular solutions clearly).
This problem tests technical skill (differentiation, algebra) and strategic insight (resonance recognition), making it a challenging but fair exam question.
nice
what was your prompt? did you run it locally (if so, which model?)
Wild! Deepseek W
Wow, what was the prompt you used?
@ prompt:
if d^2x/dt^2 +2dx/dt +5x = 4e^-t(cos2t+sin2t), x(0)=1, x'(0) = 2
find x(t)
@PagManProductions Legend, thank you
u know it a good day when neil drops this banger
23:47 i think you forgot to multiply by (1-t) for product rule, however it didn't affect the final answer which is noice
I'll take your word for it, I was probably hallucinating at that point 🤣
Why doesn’t the particular integral also have another constant as PI for 4e^-t is ke^-t isn’t it? Not just e^-t
disgusting question bruh so easy to make a silly mistake anywhere that whole time
Yeah for sure, I was sweating the whole time I can't lie
Use Laplace transformation and turn the whole thing to a simple algebraic computation and get the answer easier
Asked bro what he had for breakfast and told me what he had for lunch and dinner
@@NeilDoesMathsI just added the comment to motivate some interested user to seek and try getting the solution using an alternative method.
Nasty question !
That question belongs on an English Essay Quesrion
it gives you x, cant you find x’ and x’’ and substitute instead
that would be the dream... but if they want you to show a result, you cannot use that as part of your answer... they would have to say "if x=... then show ax''+bx'+cx=..."
What paper was this from?
No idea... I just kept getting tagged on tiktok
im only in year 12 rn, i am NOT ready for year 13🙏
This is such a mean question sooo easy to make silly mistakes. I remember getting a non-homogeneous 2nd order de on my further maths last year but was not as mean as this.
these examiners were having a bad day in the office clearly
10 billion product rules
what exam board was this?
Not sure I was just tagged on TT 😂
what exam even has a 25 mark question? edexcel only gives, like , 10 marks max for a singular part.
Further maths is a little different.
@@tameen3907 yes im talking about further maths. 25 mark questions are unheard of. that is 1/3 of the paper. FM papers out of 75 marks fyi
lol exactly, I am giving CIE Further Maths, and they never give more than 11 marks for a 2nd order DE.
Lost me on the first line mate. Not looking good
I'll do better next time