DE Chapter 1

Question 1

Differential equation (DE)

Answer 1

A differential equation (DE) is an equation involving a function and some of its derivatives. When the derivatives are only ordinary derivatives (such as y’, y’’, y’’’, etc.), we call the equation an ordinary differential equation. (If the equation involves any partial derivatives, we call it a partial differential equation.)

Question 2

Solution to a differential equation

Answer 2

A solution to a differential equation is a function that when substituted into the differential equation yields a true equation.

Question 3

Order of a differential equation

Answer 3

The order of a differential equation is the order of the highest derivative that appears in the equation.

Question 4

Slope Field

Answer 4

The slope field of direction field of a first order differential equation is a graph consisting of line segments whose slope at a point (x0 y0) is obtained by substituting the coordinates of the point into the differential equation and solving for the derivative. The line segment with this slope is positioned at (x0, y0)

Question 5

Linear differential equation

Answer 5

A linear differential equation is one of the form
a_n(x) y^(n) + a_(n-1)(x) y^(n-1) + … + a1(x) y’ + a0(x) y = g(x)
Each coefficient function ai(x) is a function of only the independent variable as is g(x).