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zip@zip.com
science forum beginner

Joined: 29 May 2005
Posts: 2

Posted: Sun May 29, 2005 1:04 am    Post subject: y' = (x + y - 1)^2 .....help

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
William Elliot
science forum Guru

Joined: 24 Mar 2005
Posts: 1906

Posted: Sun May 29, 2005 1:35 am    Post subject: Re: y' = (x + y - 1)^2 .....help

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...

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?
Jim Spriggs
science forum Guru

Joined: 24 Mar 2005
Posts: 761

Posted: Sun May 29, 2005 5:41 pm    Post subject: Re: y' = (x + y - 1)^2 .....help

"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}.
Jim Spriggs
science forum Guru

Joined: 24 Mar 2005
Posts: 761

Posted: Sun May 29, 2005 5:50 pm    Post subject: Re: y' = (x + y - 1)^2 .....help

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'.

Should be

u' = 1 + y'
etc.

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