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First Year Mathematics B (Integration, Series, Discrete Maths & Modelling) (1 Viewer)

InteGrand

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Re: MATH1231/1241/1251 SOS Thread

Lol they made us solve this differential equation by considering how it is an exact ODE. But the solution y=Ax just bugs me... is there a shorter way to doing this one haha

Note the LHS is d/dx (y/x).
 

RenegadeMx

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Re: MATH1231/1241/1251 SOS Thread

divide by e^x cos(y) a bit of rearrange you should get -cot(y)dy=dx
 

leehuan

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Re: MATH1231/1241/1251 SOS Thread

This is boring and tiring. What is the giveaway as to what values of p and q I am supposed to pick.

 

Paradoxica

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Re: MATH1231/1241/1251 SOS Thread

This is boring and tiring. What is the giveaway as to what values of p and q I am supposed to pick.

Remember that d/dz z^n = nz^(n-1), I think that should help you...

In this case, xy² ???
 
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leehuan

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Re: MATH1231/1241/1251 SOS Thread

Remember that d/dz z^n = nz^(n-1), I think that should help you...
It's hard to juggle that when I have to consider two constants at a time and not just one
 

Paradoxica

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Re: MATH1231/1241/1251 SOS Thread

It's hard to juggle that when I have to consider two constants at a time and not just one
y is on the right, and there is a 3, so you want 3y². x is on the left and you have 4x² so you want 4x³. so xy² is a possibility...
 

leehuan

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Re: MATH1231/1241/1251 SOS Thread

I can't identify the type of this one...



...unless I did my partial derivatives wrong
 

leehuan

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Re: MATH1231/1241/1251 SOS Thread

make dy/dx the subject and you'll see.

substitution y(x)=x.v(x)
Oh crap I forgot about that g(y/x) because they said they'd give us the substitution in the exam
 

leehuan

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Re: MATH1231/1241/1251 SOS Thread





Part a) was quite ok

Part b)... what? How does that even work
 

leehuan

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Re: MATH1231/1241/1251 SOS Thread

Just out of curiosity, what's an example of a first order linear ODE that's also exact?

Or does this not exist
 

InteGrand

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Re: MATH1231/1241/1251 SOS Thread

Of course, an obvious and trivial example would be the ODE 0y + y' = 0, i.e. y' = 0.
 

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