Differential equation is an equation involving derivatives of a dependent variable with respect to one or more independent variables.
Example: d²y/dx²+ y = x²
Order and degree are two attributes of a differential equation.
The order of a differential equation is the order of the highest differential coefficient involved. If second order derivative is present in the differential equation, the order of the equation is two or it is of second order. The equation give above as an example is a second order equation as d²y/dx² a second order derivative of y is present in the equation.
In the equation, the power to which the higher differential coefficient or derivative is raised is known as the degree of the equation.
Examples (d³y/dx³)4 + (d²y/dx²)² +y² = 0 is a 3rd order and 4th degree equation. 3rd order because d³y/dx³ is present in the equation and it is the highest order derivative in the equation. 4th degree because d³y/dx³ is raised to the fourth power.