Section 9: Differential Equations

Question 1

Differential equation

Answer 1

An equation that contains an unknown function and one or more of its derivatives.

Question 2

Order of a differential equation

Answer 2

The order of the highest derivative that occurs in the equation.

Question 3

Solution to a differential equation

Answer 3

Function f is called a solution if the equation is satisfied when y = f(c) and its derivatives are substituted into the equation.

Question 4

Autonomous differential equation

Answer 4

An equation where the slopes corresponding to two different points with the same y-coordinate must be equal.

Question 5

Seperable equation

Answer 5

A first order differential equation in which the expression for dy/dx can be factored as a function of x times a function of y.

Question 6

Orthogonal Trajectory of a family of curves

Answer 6

A curve that intersects each curve of the family orthogonally, that is, at right angles.

Question 7

First-order linear differential equation

Answer 7

Can be put in the form:

y’ + P(x)y = Q(x)

Question 8

How to solve a linear differential equation

Answer 8

Multiply both sides by the integrating factor I(x) = e^(integral of P(x)dx)