First-Order DifferentialEquations

First-Order DifferentialEquations

1. STANDARD FORM AND DIFFERENTIAL FORM: y'=f(x,y)

2. LINEAR EQUATIONS :If f(x,y) can be written as f(x. y) = —p(x)y + q(x) (that is, as a function of x times y. plus another function of x). the differential equation is linear.

3. Bernoulli differential equation is an equation of the form: y^'+p(x)y=q(x)y^n where n denotes a real number. When n = 1or n = 0. a Bernoulli equation reduces to a linear equation.