PX153 - C1 - introduction and definitions

ordinary differential equation (ODE)

definition

• contains only ordinary derivatives, no partial derivatives
• order of an ODE is the order of the highest derivative
• degree of an ODE is the power to which the highest derivative is raised, with all derivatives as integer powers
• so an equation of the form $\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}+c=0$ with solution $y(x)$ is a second order, first degree ODE, where $y$ is a dependent variable, x is an independent variable, and c is a constant

general solution

• the most general function that satisfies the ODE
• contains all possible solutions
• the general solution of an $n^{th}$ order ODE will contain $n$ constants of integration which needs $n$ boundary conditions

particular solution

• satisfies the ODE subject to these boundary conditions