Math 45 Question Flashcards

What do we mean by the order of a differential equation?

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

What does it mean for a first-order ODE to be exact?

A first order ODE is said to be exact if there exists a (smooth) function w(x,y) such that partialw/partialx = M (x,y) and partialw/partialy = N(x,y).

What does it mean for a first-order ODE to be separable?

A first order ODE is said to be seperable if it can be written down in the form of

dy/dx = g(x)h(y)

What does it mean for a first-order ODE to be autonomous?

An autonomous first order ODE is one that can be written in the form dy/dt = f(y). In other words it does not have t in it.

What do we mean by an equilibrium solution of an autonomous first-order ODE?

This means that the solution does not change with time.

What do we mean by an integral transform?

An integral transform is an operator that takes the form of one type of function such as t, then spits out an output in the form of functions of s.

Are all autonomous ODE’s seperable?

Yes

What was the MATLAB command introduced in class for numerically solving first-order ODEs?

Dsolve(eqn,cond)

How do we write e^2x in matlab

exp(2*x)