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## Differential Equations

by: Diana Prosacco

12

0

1

# Differential Equations MATH 225

Diana Prosacco
GPA 3.9

Staff

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COURSE
PROF.
Staff
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Class Notes
PAGES
1
WORDS
KARMA
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## Popular in Mathematics (M)

This 1 page Class Notes was uploaded by Diana Prosacco on Monday October 5, 2015. The Class Notes belongs to MATH 225 at Colorado School of Mines taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/219616/math-225-colorado-school-of-mines in Mathematics (M) at Colorado School of Mines.

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Date Created: 10/05/15
18 Linearity Principles Linearity Principle If yht is a solution of the homogeneous linear equation dy may or i g my 0 then kyht is a solution for any constant k Extended Linearity Principle Consider the nonhomogeneous equation d d z aty bt and its associated homogeneous equation d y aty O 1 If yht is any solution to the homogeneous equation and ypt is any solution to the nonhomogeneous equation then yht ypt is also a solution of the nonhomogeneous equation 2 Suppose ypt and yqt are two solutions of the nonhomogeneous equation then ypt yqt is a solution of the homogenous equation Therefore if yht is nonzero kyht ypt is the general solution of the nonhomogeneous equation

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