       Re: change the solution to a differential equation into a user defined function - question.nb (0/1)

• To: mathgroup at smc.vnet.net
• Subject: [mg15603] Re: change the solution to a differential equation into a user defined function - question.nb (0/1)
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 28 Jan 1999 04:23:31 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <786u4u\$29b@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Young

sol=DSolve[y'[x]==x,y[x],x]

To make a pattern for the solution we have to do  replace y[x] by y[x_]
and -> by := so  we can write down

holdsol=(Hold /@
Flatten[sol/.
HoldPattern[Rule[z_,b_]] :>
Rule@@ {z /. x-> Pattern[x,Blank[]],b}]) /. Rule
->SetDelayed

The result is a list of function definitions enclosed by Hold and you
have to
decide which solution you want. If there is only one solution you can
make type

ReleaseHold[
holdsol[]
]

and see that you have the defintion for the pattern y[x_]

Hope that helps
Jens

Yong Cai wrote:
>
> I probably have to apologize for the awkward name for the subject.
>
> My question is

> When I define the same function for y[x] by myself, it is evidently  a
> pattern where x can be taken in any value.
>
> Then comes the question: how can we use the solution given in a
> differential equation which itself is a function as a function for
> later use?
>
> It seems to be straightforward, but I have looked through the
> Mathematica Book and found no clue. Your help will be greatly
> appreciated.

```

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