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[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.