Definitions

Question 1

What is a homogeneous DE

Answer 1

All terms involve only the dependent variable and its derivatives

Question 2

What is the order of a DE?

Answer 2

the highest “power” (prime) derivative in a DE

Question 3

What is a linear DE?

Answer 3

Variable has power of 1, only multipled by constants (can apply to 1 variable in an eq instead of entirety)

Question 4

What is a separable DE?

Answer 4

variables can be rearranged to be on either side of =

Question 5

What is an autonomous DE?

Answer 5

y’ = f(y) [no independant variable]

Question 6

What are equilibrium solutions of a DE?

Answer 6

Solution of y’ = 0

Question 7

What is a non-linear DE?

Answer 7

Variable does not have power of 1, and can be multiplied by variables

Question 8

What is a non-homogenous DE?

Answer 8

Ly = f(x) where f(x) is a function not involving y

Question 9

What is the format of a non-homogenous DE?

Answer 9

y’’ + p(x)y’ + q(x)y = g(x)

Question 10

What is the format of a Bernoulli equation?

Answer 10

y′ + p(x)y = q(x)y^n

Question 11

What is the format of a homogenous DE?

Answer 11

y’’ + p(x)y’ + q(x)y = 0