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zip@zip.com
science forum beginner
Joined: 29 May 2005
Posts: 2
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 Posted: Sun May 29, 2005 1:04 am Post subject:
y' = (x + y - 1)^2 .....help
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Task is to solve following differential equation problem with proper
substituion which is NOT given
y' = (x + y - 1)^2
if it's not problem please comment it...
tnx |
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William Elliot
science forum Guru
Joined: 24 Mar 2005
Posts: 1906
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| Posted: Sun May 29, 2005 1:35 am Post subject:
Re: y' = (x + y - 1)^2 .....help
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On Sun, 29 May 2005, zip@zip.com wrote:
| Quote: | Task is to solve following differential equation problem with proper
substitution which is NOT given
Oh you poor dear, having to find a substitution by yourself with no |
more than just your intuition, creative insight and trial and error.
| Quote: | y' = (x + y - 1)^2
if it's not problem please comment it...
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It is a problem and the problem is to find the substitution.
My first attempt was u = y - 1, which wasn't satisfactory.
My second attempt was, ... but don't let me spoil your fun.
What substitutions have you tried and with what results? |
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Jim Spriggs
science forum Guru
Joined: 24 Mar 2005
Posts: 761
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| Posted: Sun May 29, 2005 5:41 pm Post subject:
Re: y' = (x + y - 1)^2 .....help
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"zip@zip.com" wrote:
| Quote: |
Task is to solve following differential equation problem with proper
substituion which is NOT given
y' = (x + y - 1)^2
if it's not problem please comment it...
tnx
|
Put
u = x + y - 1
(the plan is simple: get rid of the least pleasant parts of the original
DE)
then
u' = y'.
The DE becomes
u' = u^2
int u^{-2} du = int dx
-u^{-1} = x - C
u = (C - x)^{-1}
x + y - 1 = (C - x)^{-1}
y = 1 - x + (C - x)^{-1}. |
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Jim Spriggs
science forum Guru
Joined: 24 Mar 2005
Posts: 761
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| Posted: Sun May 29, 2005 5:50 pm Post subject:
Re: y' = (x + y - 1)^2 .....help
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Jim Spriggs wrote:
| Quote: |
"zip@zip.com" wrote:
Task is to solve following differential equation problem with proper
substituion which is NOT given
y' = (x + y - 1)^2
if it's not problem please comment it...
tnx
Put
u = x + y - 1
(the plan is simple: get rid of the least pleasant parts of the original
DE)
then
u' = y'.
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Should be
u' = 1 + y'
etc. |
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