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

• To: mathgroup at smc.vnet.net
• Subject: [mg15566] change the solution to a differential equation into a user defined function - question.nb (0/1)
• From: yc10 at acpub.duke.edu (Yong Cai)
• Date: Tue, 26 Jan 1999 13:44:45 -0500 (EST)
• Organization: Duke University, Durham, NC, USA
• Sender: owner-wri-mathgroup at wolfram.com

```I probably have to apologize for the awkward name for the subject.

My question is

In:=
sol=DSolve[y'[x]==x,y[x],x]
Out=
\!\({{y[x] \[Rule] x\^2\/2 + C}}\)

In:=
FullForm[sol]
Out//FullForm=
List[List[Rule[y[x],Plus[Times[Rational[1,2],Power[x,2]],C]]]]

After I type in the command to solve the differential equation, I am
given a replacement rule of y[x], which can be applied as a rule when
the argument inside y is x, nothing else.

In:=
y[x_]:=x^2/2+c
In:=
FullForm[y[x_]]
Out//FullForm=
Plus[c,Times[Rational[1,2],Power[Pattern[x,Blank[]],2]]]

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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