- The order of a differential equation is the highest order derivative in the equation
- The degree of a differential equation is the highest power of the highest order derivative in the equation
- The order and degree of a differential equation can affect the complexity of its solution
- Most commonly encountered differential equations are first or second order, but higher order equations are also possible
- It is important to correctly identify the order and degree of a differential equation before attempting to solve it
Important Formulas to Remember in these topic
The order of a differential equation is the highest derivative that appears in the equation, such as:
$$\frac{d^2y}{dx^2} + \frac{dy}{dx} = 0$$
The degree of a differential equation is the power to which the highest derivative is raised, after the equation has been written in standard form, such as:
$$\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^3 + y = 0$$