Symmetry in Differential Equations Discussion

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Part I: Introduce differential equations. What is a differential equation? How are differential equations used in mathematics, science, and engineering to solve problems?

Part II: Define symmetry in differential equations. Discuss how symmetry is used to solve certain types of differential equations. Part III: Solve two differential equations using symmetry methods. Present a clear analysis of your solutions.

Part IV: Make some concluding remarks about the importance of symmetric methods in the solution of differential equations.

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Running head: DIFFERENTIAL EQUATIONS PAPER

Differential Equations Paper
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DIFFERENTIAL EQUATIONS PAPER

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Contents
Part 1. What is a differential equation? .............................. Error! Bookmark not defined.
Definition of a differential equation .............................. Error! Bookmark not defined.
Applications of differential equations ............................ Error! Bookmark not defined.
Part 2. What is symmetry in a differential equation? .........Error! Bookmark not defined.
Definition of symmetry in a differential equation .........Error! Bookmark not defined.
Bilinearity in a differential equation .............................. Error! Bookmark not defined.
Application of symmetry to solve differential equations ............. Error! Bookmark not
defined.
Part 3. Examples of solutions of differential equations using the symmetry method Error!
Bookmark not defined.
Example 1 ......................................................................Error! Bookmark not defined.
Example 2 ......................................................................Error! Bookmark not defined.
Part 4. Conclusions ............................................................ Error! Bookmark not defined.
References ..........................................................................Error! Bookmark not defined.

DIFFERENTIAL EQUATIONS PAPER

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