CHAPTER 1 Flashcards
Application of De
Exponential growth (Population)
Exponential Reduction or Decay
The ____ of a D.E. is the same as the order of the highest-ordered derivative in the equation.
order
The _____ of a D.E. is the same as the power (or exponent) to which the derivative of the highest order in the equation is raised.
degree
A D.E. may be ______ or ______ as to the type of derivatives or differential appearing on the equation.
ordinary/partial
The ______ is the relation involving only the variables and arbitrary constants, free of any
derivatives of differential, and consistent with, or satisfying, the given D.E
solution to a D.E.
The most general solutions of a D.E. of the nth order contains_________.
arbitrary constants
An ________ involves function and its derivatives. It contains only one independent variable and one or more of its derivatives with respect to the variable
ordinary differential equation
A differential equation containing partial derivatives of the dependent variable (one or more) with more than one independent variable.
Partial differential equation
A differential equation of the form
𝒅𝒚/𝒅𝒙 + 𝑷𝒚 = 𝑸,
where P and Q are constants or functions of x only is called a ________ differential equation.
first order linear
In a system of differential equations used to describe a time-dependent process, a ________ is a function that appears in the equations and is only a function of time, and not of any of the other variables.
forcing function
A ____ differential equation does not combine y or any of its derivatives through multiplication.
linear
_______ contains functions of one of the dependent variable on its derivatives such as:
Trigonometric functions, Exponential functions, Logarithmic functions
Non-linear ODE
A linear differential equation is ______ if the forcing function g(x) is 0.
homogenous
The graph of the solutions of a differential equation are called its )_______
integral curves
A solution of an ordinary differential equation of order n that involves exactly n essential arbitrary constants called also complete solution, general integral
General Solution
A solution of a partial differential equation that involves arbitrary functions.
General Solution
A ______ of a differential equation is a solution obtained from the General Solution by assigning
specific values to the arbitrary constants
Particular Solution
sets the initial condition of the problem, normally at zero value of the independent variable, to obtain the value of the arbitrary constant
Initial Value Ploblem
The term _______ is used when the independent variable is the time and the condition given is at zero-time, t=0
initial condition
The term ______ is used if the independent variable is anyone of the spatial coordinates x, y or z and the
conditions given are for known values of anyone of these coordinates
boundary
In application, an _____ is a result of the magnitude (dependent) of the function observed at any given time (independent)
arbitrary constant
The graph of a solution of a differential equation is a ________.
solution curve
The number of derivatives of the produced differential equation should be ______ to the number of distinct
arbitrary constants to be eliminated
equal
