DIFFEQ EXAM 1

Autonomous differential equation

ex: y’=t is NOT autonomous because the right hand side doesn’t depend on the unknown (which is y

How do you find an equilibrium point?

What is a phase line and how do you create one

A phase line tells how the solution would move in each interval

What are the three types of equilibrium points on a phase line

What would the process be to create the phase line for this DE

If the arrow is right, y(t) is a positive value when you plug in the critical point

What’s the order of the following ODE and why

2nd bc theres a second derivative

What’s a linear ODE

When the y (unknown) is only multiplied by constants or ordinary functions (NOT BY Y ITSELF). sin(y) and e^y are NONLINEAR, but sin(x) and e^x are fine bc theyre not of the unknown

which of these are linear

What is standard form of a DE

Is this linear, autonomous, in standard form, 2nd order?

When is a first order DE separable

If it can be separated into two functions with their own parameter

How do you solve a separable IVP?

What’s the standard form for a linear ODE

What’s the integrating factor for a linear ODE

Is this DE separable or linear? Depending on which, what should be done?

Therefore proceed with linear DE operation (using the integration factor)

This is not separable; follow through with linear procedure