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DE: quick help

Theirs just a few things that regularly pop up in DE exams that i could really use help understanding

1. When a v randomly appears in newtons 2nd law next to the acceleration and mass like in question 2 (i) of this paper.

http://www.mei.org.uk/files/papers/de_june_2012.pdf

2. When it says y is bounded as x tends to infinity i don't know how you would use this information, like in question 1 (ii) of this paper.

http://www.ocr.org.uk/Images/144670-question-paper-unit-4758-01-differential-equations.pdf

Any help would be greatly appreciated :smile:
Reply 1
Original post by Mrbrian
Theirs just a few things that regularly pop up in DE exams that i could really use help understanding

1. When a v randomly appears in newtons 2nd law next to the acceleration and mass like in question 2 (i) of this paper.

http://www.mei.org.uk/files/papers/de_june_2012.pdf


a=dvdt=dxdtdvdx=vdvdxa=\frac{dv}{dt}=\frac{dx}{dt} \frac{dv}{dx} =v \frac{dv}{dx}

As for your other question, could you post your general solution? Without looking at the question I'd say that if it's bounded certain constants will need to be zero.
Original post by Mrbrian
Theirs just a few things that regularly pop up in DE exams that i could really use help understanding

1. When a v randomly appears in newtons 2nd law next to the acceleration and mass like in question 2 (i) of this paper.

http://www.mei.org.uk/files/papers/de_june_2012.pdf

2. When it says y is bounded as x tends to infinity i don't know how you would use this information, like in question 1 (ii) of this paper.

http://www.ocr.org.uk/Images/144670-question-paper-unit-4758-01-differential-equations.pdf

Any help would be greatly appreciated :smile:


For the second question, If you have a solution of the form y=Aek1x+Bek2xy=Ae^{k_1x}+Be^{k_2x} with k1>0 and k2<0k_1 >0 \mathrm{\ and\ }k_2 <0 then the solution can only be bounded as x+ if A=0 x \rightarrow +\infty \mathrm{\ if\ }A=0 Similarly for x we would require B=0. x\rightarrow -\infty \mathrm{\ we\ would\ require\ } B=0.
Reply 3
Thanks guys :smile:

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