Section 2.1

First Order Linear Differential Equations

General form:

$$\frac{dy}{dt} = f(t,y)$$

First Order: Involving only the first derivative

Linear: f(t,y) is a linear function in y

i.e. f(t,y) = p(t)y + g(t), for some functions p and g.

Examples: First Order Linear

$$\frac{dy}{dt} + \frac{1}{2}y = \frac{3}{2}$$

$$y' = t^{100}y + \pi$$

$$e^x \frac{dy}{dx} = 9xy + .00007$$