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# differential equation watch

1. struggle with part b and c

any suggestions

2. Part (b):

differentiate W(x) using product rule:

Spoiler:
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The question tells you that both y1 and y2 are solutions to the differential equation, so plug them into it

Spoiler:
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Now you've got two equations from putting in y1 and y2, multiply each equation by y2 and y1 respectively.

Now you've got all the equations you need, now you need to manipulate them to get the required expression...
3. so by the product rule.

, then you want to use the fact that

and and it should fall out, let me know if it doesn't.

As for (c) you just need to differentiate both and plug into and you end up with which simplifies to
4. Part (c)

You're told what y1 and y2 are, in a you worked out the determinant, so you need to find y'1 and y'2 and then plug them into your solution for a....

Spoiler:
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Use a simple trig identity and simplifies nicely.
5. (Original post by Piguy)
Part (b):

differentiate W(x) using product rule:

Spoiler:
Show

The question tells you that both y1 and y2 are solutions to the differential equation, so plug them into it

Spoiler:
Show

Now you've got two equations from putting in y1 and y2, multiply each equation by y2 and y1 respectively.

Now you've got all the equations you need, now you need to manipulate them to get the required expression...

why do we multiply each equation by y2 and y1 respectively ?
6. (Original post by Noble.)
so by the product rule.

, then you want to use the fact that

and and it should fall out, let me know if it doesn't.

As for (c) you just need to differentiate both and plug into and you end up with which simplifies to

as previous state, why do we multiply each equation by y2 and y1 respectively ?
7. (Original post by NightKings)
as previous state, why do we multiply each equation by y2 and y1 respectively ?
Because you want to show which you can only do by using the fact are solutions of the second-order homogeneous equation. You can either sub one of the values in, it's equivalent to multiplying both equations by the other solution.
8. Where is this from? Looks very interesting. Is this AEA?
9. (Original post by Sinfire)
Where is this from? Looks very interesting. Is this AEA?
Unless standards have vastly improved, this question is definately not at the school level, be it A-Level, MAT, AEA, STEP or Olympiad. Wronskian is not something mentioned pre uni.

If I'm not mistaken, it's 1st year undergrad, perhaps even 2nd year at some places.
10. (Original post by sello)
Unless standards have vastly improved, this question is definately not at the school level, be it A-Level, MAT, AEA, STEP or Olympiad.

If I'm not mistaken, it's 1st year undergrad, perhaps even 2nd year at some places.
I'm not at uni yet, but I've seen some of the homework that 1st year undergrads get This is definitely much easier than what I've seen. Then again I've seen analysis... and I don't know analysis.

Also, does AEA require further maths? If not, this can't be AEA...
11. (Original post by sello)
Unless standards have vastly improved, this question is definately not at the school level, be it A-Level, MAT, AEA, STEP or Olympiad. Wronskian is not something mentioned pre uni.

If I'm not mistaken, it's 1st year undergrad, perhaps even 2nd year at some places.
Oh and from my experience, they can do that in STEP. They introduce some unfamiliar concept and then make you use it.
12. Yeah, to be honest, the question is about similar difficulty to AEA/STEP, not undergrad. maths.
13. (Original post by NightKings)
why do we multiply each equation by y2 and y1 respectively ?
Because then between the equations you have the common term

which you can then get rid of, as the equation they want you to derive has to q(x) in it.
14. (Original post by Sinfire)
I'm not at uni yet, but I've seen some of the homework that 1st year undergrads get This is definitely much easier than what I've seen. Then again I've seen analysis... and I don't know analysis.
This looks like a first-year undergrad question, but it's the sort of thing that would typically be taught as part of a Methods / Differential Equations course rather than as part of a rigorous Analysis course (that's not to say you can't prove rigorous results about DEs - there are plenty of complicated theorems about existence and uniqueness of solutions etc - but this question is really just an algebra bash!).
15. (Original post by Sinfire)
I'm not at uni yet, but I've seen some of the homework that 1st year undergrads get This is definitely much easier than what I've seen. Then again I've seen analysis... and I don't know analysis.

Also, does AEA require further maths? If not, this can't be AEA...
In the "old" days, S-Levels were based on the A-Level syllabus but harder questions, so S-Level maths did not require additional topics found in further but S-level further maths obviously did.

I suspect the same is for AEAs.

When you say analysis, I think you mean the idea behind limits, riemann integrals, etc. That is a branch of pure maths.

This question is definately not pure maths but in the area of applied, vector calculus, etc.

I do agree that it seems somewhat "easy" by undergrad standards.

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