A bit of differential equation maths, i'm shtuck Watch

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byb3
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#1
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My mate from an engineering course asked for some help on a few of these, but this one has me stuck.

y'' - y = 8t*e^t

I get the first bit:

Y = Ae^x + Be^(-x)

But I can't see what to put as Yp, so y'' - y = 8t*e^t

I've tried at*e^t and at^2*e^t plus a few others, but they always seem to cancel out.

Can anybody give me a push in the right direction?

Adam
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bono_3
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(Original post by byb3)
y''
Sorry, I can't be of any help, but may I ask what is y" ? :confused:
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Juwel
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(Original post by bono_3)
Sorry, I can't be of any help, but may I ask what is y" ? :confused:
Second derivative, d²y/dx².
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Expression
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(Original post by bono_3)
Sorry, I can't be of any help, but may I ask what is y" ? :confused:
The second differential. In the same way as d2y/dx^2 is the second differential, tis just Lebonitz and Newton having different ways of doing things.
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byb3
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(Original post by bono_3)
Sorry, I can't be of any help, but may I ask what is y" ? :confused:
Its second order.

I got it like 10 seconds after posting.

Yp = (a*t^2-a*t)*e^t

This cancels out right.

Adam
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bono_3
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(Original post by Expression)
The second differential. In the same way as d2y/dx^2 is the second differential, tis just Lebonitz and Newton having different ways of doing things.
Ahhh right - Why do they denote them differently?
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bono_3
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(Original post by byb3)
Its second order.

I got it like 10 seconds after posting.

Yp = (a*t^2-a*t)*e^t

This cancels out right.

Adam
Well done.
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Juwel
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(Original post by bono_3)
Ahhh right - Why do they denote them differently?
They both want to claim the discovery of calculus, despite that the Hindus did it long before them. So they use different symbols.
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iiikewldude
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(Original post by bono_3)
Ahhh right - Why do they denote them differently?
because the guys hated each other. Lebiniz notation make more sense to me and is more commonly used.
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byb3
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(Original post by iiikewldude)
because the guys hated each other. Lebiniz notation make more sense to me and is more commonly used.
Its used outside of England, where as in england we are usually taught the newtonian ways.

Adam
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Amazing
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(Original post by iiikewldude)
because the guys hated each other. Lebiniz notation make more sense to me and is more commonly used.
Yeah, it's certainly easier to work with. Newton did do it first though (not that that really means much considering neither of them actually copied anything from each other) and I prefer his way of looking at things. Do you know if "the calculus" was a phrase coined by Newton, or Lebiniz? I was always under the impression it was a phrase first used in The Principia, but I'm not too sure.
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CHilL
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(Original post by Amazing)
Yeah, it's certainly easier to work with. Newton did do it first though (not that that really means much considering neither of them actually copied anything from each other) and I prefer his way of looking at things. Do you know if "the calculus" was a phrase coined by Newton, or Lebiniz? I was always under the impression it was a phrase first used in The Principia, but I'm not too sure.
I think Newton introduced it as the method of fluxions.
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