Chapter 1: First Order ODEs

General Solution

Solution to differential equation containing arbitrary constants

Particular Solution

Solution that contains no arbitrary constants. When you specify the arbitrary constants in a general solution

Initial Value Problem

An ODE together with an initial condition

Bernoulli Equation

y'+p(x)y = g(x)y^a

Solution process for Bernoulli Equation

Let u = y^(1-a), differentiate and substitute

Exact ODE

Equation of the form
M(x,y)dx + N(x,y)dx = 0
is exact if there exists a function u such that
du = Mdx + Ndy

Criterion for Exactness

dM/dy = dN/dx

Solution of Exact ODEs

u =