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MathGroup Archive 2005

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Re: Problem with DSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53532] Re: [mg53513] Problem with DSolve
  • From: Selwyn Hollis <sh2.7183 at earthlink.net>
  • Date: Sat, 15 Jan 2005 21:08:16 -0500 (EST)
  • References: <200501150644.BAA25342@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On Jan 15, 2005, at 1:44 AM, Anand wrote:

> Consider this simple 1st order equation
>
> DSolve[(y'[x])^2 - x y'[x] + y[x] == 0, y[x], x]
>
> The generic solution should be y= c ( x - c)
> and in addition a singular solution of this equation is y = x2/4 .
>
> The solution Mathematica produces is different. At least I could not
> relate it to the above solutions. What am I missing?
> sincerely, -anand.


It's not different; it just needs some massaging. The following steps 
(in Mathematica 5.1) reveal  the solution y = c*(x-c).

    solns1 = Simplify[y[x]/.DSolve[y'[x]^2-x*y'[x]+y[x]==0, y[x], x]]

    solns2 = solns1 /. E^C[1] -> 2*(c+2)^2

    Simplify[solns2, Assumptions -> {x>-4, c>-2}]


Regards,

Selwyn Hollis
http://www.appliedsymbols.com


-----
Selwyn Hollis
http://www.appliedsymbols.com
(edit reply-to to reply)


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