An equation that contains derivative(s).
For example, dy/dx = 2 is a differential equation. Integration needs to be applied to solve this type of equation. Rearranging the differential equation, we have:
dy = 2dx
Integrating both sides, we obtain:
y = 2x + C
in which C is a constant of integration. As shown, the solution to a differential equation is itself an equation.
Differential equations that contain only first derivatives (dy/dx) are called first order. Those that contain second derivatives are called second order, etc. Generally, the highest derivative in the equation is the order of the differential equation.