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I explain here how I use `maple` to respond to an e-mail
query like the one below:

To: bell@math.purdue.edu From: goober@cartoon.ecn.purdue.edu Subject: HELP!!!! For the last 72 hours I have been trying to solve the equation x y' + y = 1. I'm beginning to think that it doesn't have a solution. Please help me!!! Jimmy Goober P.S. My roomate wants me to ask you what the integral of x^2 sin(7x) is.

I shall now dispose of these questions in a few simple keystrokes.
First, I start an e-mail message to Mr. Goober in an xterm using
an editor like vi. Then I fire up `maple` in another
xterm by typing

maple

NOTE: That's `maple`, not xmaple. I want the ASCII terminal version
of maple for this task.

After I type maple, I see

hua-231% maple |\^/| Maple V Release 4 (WMI Campus Wide License) ._|\| |/|_. Copyright (c) 1981-1996 by Waterloo Maple Inc. All rights \ MAPLE / reserved. Maple and Maple V are registered trademarks of <____ ____> Waterloo Maple Inc. | Type ? for help. >

Next I type the following commands at the > prompt.

> Diff(y,x) + (1/x)*y= 1/x; dy -- + y/x = 1/x dx > u(x)= exp( Int( 1/x , x ) ); / | u(x) = exp( | 1/x dx) | / > Int( x^2 * sin(7*x) , x) = int( x^2 * sin(7*x) , x ) + C; / | 2 2 | x sin(7x) dx = - 1/7 x cos(7x) + 2/343 cos(7x) + 2/49 x sin(7x) + C | /

To answer Mr. Goober in a prompt and courteous fashion, I shall click with my left mouse button at the start of a portion of maple output that I want to copy to my e-mail and then I shall click with the right mouse button at the end of the text to select it. Then I shall click with the middle mouse button while in input mode of vi in my e-mail to insert the selected text from maple in the e-mail. (If you're a dexterous mouser, you can left mouse click and drag over the text to select it ---and then right mouse click to adjust the ending point.)

Note: If you use vi, you'll want to set your *wrapmargin* to zero
before you glob text into your file with the middle mouse button.
To do this, simply type

`
:set wm=0
`

in command mode of vi.

Here is the result of my efforts:

Dear Mr. Goober, Notice that you can divide your ODE by x to obtain dy -- + y/x = 1/x , dx a first order linear ODE in standard form. The integrating factor will be / | u(x) = exp( | 1/x dx ) = x . | / Use this as in Section 1.3 of B & D to get the solution in the back of the book. See you in class on Monday? P.S. Tell your roomate / | 2 2 | x sin(7x) dx = - 1/7 x cos(7x) + 2/343 cos(7x) + 2/49 x sin(7x) + C | /

As you can see, this is also a nice way to display mathematics on the web. That last equation was set in HTML via

<P> <PRE> / | 2 2 | x sin(7x) dx = - 1/7 x cos(7x) + 2/343 cos(7x) + 2/49 x sin(7x) + C | / </PRE>

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