## Differential Equations - Initial Value Problems...

The attached document shows you how to solve an initial value problem. Moreover, it shows you how to use Maple's ODE analyzer which makes it really fast and easy to solve and plot the solutions of differential equations.

## Entering expressions in Forums...

Maple's powerful notation allows you to enter math expressions that look natural.

The following steps will show you how easy it is to write expressions.

Example 1:  Write

1. If you're on the Student Center forums, click on the red maple leaf to insert maple ma

## ... Enter a function?...

In Maple, suppose we would like to enter the function and we want to know what the function is at .

Below are a few simple steps that will show you how to achieve this.

1. Make sure you're in math mode. Type , followed by a colon and an equal sign . The colon-equals notation assigns the content on the right-hand side to a variable name on the left-hand side. I

## Make Secret Codes (Elementary Cryptography)...

Maple is amazing at making secret codes.

First, let's learn two quick words. To "encrypt" a message means that you have transformed your message such that it is unreadable by others.

And to "decrypt" means to transform it back to your original message, also known as code breaking.

We will encrypt and decrypt our original message "Hello new Maple users !".

Le

## Solving Dense Linear Systems in Maple 12

by: Maple 12

Suppose you want to solve a large dense linear system AX=B over the rationals - what should you do? Well, one thing you should probably not do is directly apply Gaussian elimination. It does O(n^3) arithmetic operations, but the size of the numbers blow up, leading to an exponential bit complexity. Don't believe me? Try it:

with(LinearAlgebra):
for N from 5 to 9 do
A := RandomMatrix(2^N, 2^N+1,generator=-10^5..10^5):
TIMER := time(GaussianElimination(A...
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