DE: DEFINITION OF TERMS

CHAPTER 1 AND 2

DIFFERENTIAL EQUATION

AN EQUATION WHICH CONTAINS ONE OR MORE TERMS AND THE DERIVATIVES OF ONE VARIABLE WITH RESPECT TO THE OTHER VARIABLE

DEPENDENT VARIABLE

ONE THAT DEPENDS ON THE VALUE OF SOME OTHER NUMBER

NUMERATOR

LOOKING FOR THE DEPENDENT VARIABLE IN DIFFERENTIAL EQUATION, YOU WOULD BASE IN ___

INDEPENDENT VARIABLE

VARIABLE THAT STANDS ALONE AND ISN'T CHANGED BY THE OTHER VARIABLES YOU ARE TRYING TO MEASURE

DENOMINATOR

LOOKING FOR THE INDEPENDENT VARIABLE IN DIFFERENTIAL EQUATION, YOU WOULD BASE IN ___

F(X)

DENOTES THE FUNCTION

ORDINARY DIFFERENTIAL EQUATION AND PARTIAL DIFFERENTIAL EQUATION

TYPES OF DIFFERENTIAL EQUATION

ORDINARY DIFFERENTIAL EQUATION

AN EQUATION IN WHICH ALL DIFFERENTIAL COEFFICIENTS HAVE REFERENCE TO A SINGLE INDEPENDENT VARIABLE

PARTIAL DIFFERENTIAL EQUATION

AN EQUATION IN WHICH CONTAINS TWO OR MORE INDEPENDENT VARIABLES AND PARTIAL DERIVATIVES

DEGREE

EXPONENT OF THE HIGHEST DERIVATIVE OCCURING IN IT, AFTER THE EQUATION HAS BEEN EXPRESSED IN A FORM OF FREE FORM RADICALS

ORDER

HIGHEST DERIVATIVE APPEARING IN IT

LINEAR DIFFERENTIAL EQUATION

AN EQUATION IN WHICH THE DEPENDENT VARIABLE AND ITS DERIVATICES OCCUR ONLY IN THE 1ST DEGREE

NON-LINEAR DIFFERENTIAL EQUATION

A DIFFERENTIAL EQUATION WHICH DOES NOT HAVE THE FORM OF THE LINEAR DIFFERENTIAL EQUATION

VARIABLE SEPARABLE

ALL TERMS CONTAINING X AND Y MUST BE GROUPED WITH DX AND DY RESPECTIVELY

GENERAL SOLUTION

CONTAINS ARBITRARY CONSTANTS WHICH IS NOT YET DEFINED

ARBITRARY CONSTANT

A SYMBOL TO WHICH VARIOUS VALUES MAY BE ASSIGNED BUT WHICH REMAINS UNAFFECTED BY THE CHANGES IN THE VALUES OF THE VARIABLES OF THE EQUATION

C

DENOTES THE ARBITRARY CONSTANT

PARTICULAR SOLUTION

A SOLUTION IN WHICH ARBITRARY CONSTANT IS DEFINED

DY/DX

Y'

EXACT EQUATION

TYPE OF DIFFERENTIAL EQUATION THAT CAN BE SOLVED WITHOUT THE USE OF SPECIAL TECHNIQUES IN THE SUBJECT

MDX + NDY = 0

EXACT EQUATION

TEST FOR EXACTNESS

MDX + NDY = 0

X

WHAT IS CONSTANT IN ∂M/∂Y

Y

WHAT IS CONSTANT IN ∂N/∂X

Y IS CONSTANT

RULE IN ∫MDX

WITHOUT X TERM

RULE IN ∫NDY

LINEAR DIFFERENTIAL EQUATION

AN EQUATION CONTAINING A VARIABLE, ITS DERIVATIVES, AND FEW MORE FUNCTIONS OF DEGREE ONE

DY/DX + P(X)Y = Q(X)

GENERAL FORMATION FOR LINEAR DIFFERENTIAL EQUATION

YE^∫P(X)DX = ∫Q(X)E^∫P(X)DX DX

FORMULA FOR LINEAR DIFFERENTIAL EQUATION