Examples:

Which of the following are ordinary differential equations?
a. $\frac{d y (t)}{d t} = λ y (t)$ exam1.gif
b. $\frac{d^{2} y (t)}{d t^{2}} + ω^{2} y (t) = f (t)$ exam2.gif
c. $\frac{d y (x, t)}{d t} - D \frac{d^{2} y (x, t)}{d x^{2}} + ω^{2} y (x, t) = f (x, t)$ exam3.gif

a. $\frac{d y (t)}{d t} = λ y (t)$ exam1.gif YES, linear first order ODE
b. $\frac{d^{2} y (t)}{d t^{2}} + ω^{2} y (t) = f (t)$ exam2.gif YES, linear second order ODE, "wave equation"
c. $\frac{d y (x, t)}{d t} - D \frac{d^{2} y (x, t)}{d x^{2}} + ω^{2} y (x, t) = f (x, t)$ exam3.gif NO, linear partial differential equation, "time dependent or transient diffusion equation"

What is the solution of an ODE? A function Give two examples of common engineering subjects that involve the solution of ODEs. Radiactive decay
Chemical kinetics
Mechanics (dynamics)
Control theory
Population dynamics
Diffusion
Transient electrical circuits