]> Examples:

## Examples:

1. Which of the following are ordinary differential equations?
a. $\frac{dy\left(t\right)}{dt}=\lambda y\left(t\right)$
b. $\frac{{d}^{2}y\left(t\right)}{d{t}^{2}}+{\omega }^{2}y\left(t\right)=f\left(t\right)$
c. $\frac{dy\left(x,t\right)}{dt}-D\frac{{d}^{2}y\left(x,t\right)}{d{x}^{2}}+{\omega }^{2}y\left(x,t\right)=f\left(x,t\right)$

a. $\frac{dy\left(t\right)}{dt}=\lambda y\left(t\right)$ YES, linear first order ODE
b. $\frac{{d}^{2}y\left(t\right)}{d{t}^{2}}+{\omega }^{2}y\left(t\right)=f\left(t\right)$ YES, linear second order ODE, "wave equation"
c. $\frac{dy\left(x,t\right)}{dt}-D\frac{{d}^{2}y\left(x,t\right)}{d{x}^{2}}+{\omega }^{2}y\left(x,t\right)=f\left(x,t\right)$ NO, linear partial differential equation, "time dependent or transient diffusion equation"

2. What is the solution of an ODE?
A function
3. Give two examples of common engineering subjects that involve the solution of ODEs.