Re: Help w/ Mathematica: simple stuff
- To: mathgroup at smc.vnet.net
- Subject: [mg30783] Re: [mg30764] Help w/ Mathematica: simple stuff
- From: BobHanlon at aol.com
- Date: Wed, 19 Sep 2001 00:16:23 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 2001/9/9 8:53:53 PM, sophtwarez at yahoo.com writes:
>I'm a mathematica novice and only doing basic calculus. We have a
>question that is as follows:
>
>y[1]=a
>y'[x]=(r*y[x])/x
>
>Explain Mathematica output of...
>y[x]=ax^r
>
>I guess I don't understand what x is doing in the denominator. The
>y[1]=a part is straight forward; when x is 1 then no matter what
>constant r is it will be 1. I also know from my material that when
>y[x]=kE^rx then y'[x]=r*y[x].
>
DSolve[{y'[x] == (r*y[x])/x, y[1] == a}, y[x], x]
{{y[x] -> a*x^r}}
substituting for y[x] in y'[x] == r*y[x]/x
D[a*x^r, x] == r*(a*x^r)/x
True
Bob Hanlon
Chantilly, VA USA