ODE 1

Question 1

How to determine the order of an ODE

Answer 1

What is the highest derivative?

Question 2

How to put an ODE in normal form

Answer 2

Isolate the highest Derivative

Question 3

How to determine if a solution to an ODE is valid

Answer 3

Plug it im

Question 4

What is an IVP

Answer 4

An ODE with an initial condition

Question 5

How to solve an IVP

Answer 5

Solve the ode and then use the initial condition to solve for C

Question 6

Interval of existance

Answer 6

the largest interval over which the solution can be defined and remain a solution. IF there is any discontinuous portion then it wont work

Question 7

How to solve separable equations steps

Answer 7

Separate the variables
integrate both sides
solve for y(t) if possible

Question 8

first order linear equation form

Answer 8

x’=a(t)x+f(t)

Question 9

is an equation homogeneous?

Answer 9

if f(t) = 0 and the form is x’=a(t)x

Question 10

formula for the integrating factor

Answer 10

e^(-int(a(t))

Question 11

how to use the integrating factor

Answer 11

put the equation into the form x’-ax=f(t)
(ux)’=uf
then integrate both sides and solve for what you need

Question 12

autonomous equation

Answer 12

an equation that does not have a dependant variable

ie x’=f(x)

Question 13

how to find equilibrium points for an ODE

Answer 13

Set the equation equal to 0

Question 14

semi stable

Answer 14

1 moves in 1 moves away

Question 15

stable

Answer 15

both move towards

Question 16

unstable

Answer 16

both move away

Question 17

Eulers method

Answer 17

yk=y(k-1)+f(t(k-1),y(k-1))h

tk=t(k-1)+h