       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 -> 2*(c+2)^2

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

Regards,

Selwyn Hollis
http://www.appliedsymbols.com

-----
Selwyn Hollis
http://www.appliedsymbols.com