Re: change the solution to a differential equation into a user defined function - question.nb (0/1)
- To: mathgroup at smc.vnet.net
- Subject: [mg15598] Re: [mg15566] change the solution to a differential equation into a user defined function - question.nb (0/1)
- From: BobHanlon at aol.com
- Date: Thu, 28 Jan 1999 04:23:28 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 1/26/99 4:06:09 PM, yc10 at acpub.duke.edu writes:
>I probably have to apologize for the awkward name for the subject.
>
>My question is
>
>In[1]:=
>sol=DSolve[y'[x]==x,y[x],x]
>Out[1]=
>\!\({{y[x] \[Rule] x\^2\/2 + C[1]}}\)
>
>In[2]:=
>FullForm[sol]
>Out[2]//FullForm=
>List[List[Rule[y[x],Plus[Times[Rational[1,2],Power[x,2]],C[1]]]]]
>
>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[3]:=
>y[x_]:=x^2/2+c[1]
>In[4]:=
>FullForm[y[x_]]
>Out[4]//FullForm=
>Plus[c[1],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.
>
Clear[y];
y[x_] := Evaluate[Flatten[
DSolve[y'[x] == x, y[x], x]][[1,2]]]
{y[x], y[3], y[-3], y[0]}
{x^2/2 + C[1], C[1] + 9/2, C[1] + 9/2, C[1]}
Bob Hanlon