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

```

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