Differential Equations - really stuck Watch

maggiehodgson
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#1
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#1
The question I am trying to answer is this

Use the substitution y = x - t to rewrite dx/dt = (x-t)^2 as a differential equation in y and t. Hence
a) find the general solution of the original equation in the for x=f(t)

So far I've done this

dx/dt = y^2

dy/dt = -1 (does the x disappear?) dt= -dy

dx = -y^2 dy

x = (-y^3)/3 +c

Not looking good with respect to the answer in the book.
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Protoxylic
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You need to form a differential equation in dy/dt first and solve that, then re substitute in your (x-t)
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ghostwalker
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#3
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(Original post by maggiehodgson)

Use the substitution y = x - t

dy/dt = -1 (does the x disappear?) dt= -dy
No, the x does not disappear.

It's a good idea to look at some examples first, if you haven't already.

dy/dt = dx/dt -1
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maggiehodgson
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(Original post by Protoxylic)
You need to form a differential equation in dy/dt first and solve that, then re substitute in your (x-t)

I think I've done that haven't I?

I think I've found dy/dt = -1 BUT I did ask the question "Does the x disappear".
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davros
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(Original post by maggiehodgson)
I think I've done that haven't I?

I think I've found dy/dt = -1 BUT I did ask the question "Does the x disappear".
Not sure what you mean by "does the x disappear?".

If y = x - t then dy/dt = (dx/dt) - 1 which you can rearrange to make dx/dt the subject.
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ghostwalker
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:holmes: Think I must be invisible - my new persona seems to be working. :woo:
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maggiehodgson
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I will be reading all the posts with interest and wil reply when I've had a think.

In the meantime, thank you all.
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maggiehodgson
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#8
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Hi

Thanks for the starter. I have never done a DE using substitution before. Ghostwalker, I took your advice and watched a video on YouTube and it sorted me out.

Gosh, that took some while.
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