Moment of inertia

          Differential equations.

Differential equations are of fundamental importance in engineering mathematics, because many physical laws and relations appears mathematically in the form of such equations.
Modelling is the transition from the given physical problem to a corresponding mathematical model(equation). This is of great importance to the engineers, the physicsist and computer scientist.

Classification of Differential equations.

1. Ordinary differential equation (ODE) and partial differential equation ( PDE).

. To differentiate between an ODE and a PDE, we need to know the amount of independent variable in the equation.
. A differential equations is said to be an ODE if it has one independent variable.
i.e
 

Where y is your dependent variable and x is your independent variable.

. A differential equation is said to be a PDE, if it has more than one independent variable.

i.e

Where y is your dependent variable and r, x, v are your independent variable.

2. First order and higher orders (second, third...) Differential equations.

. We use the degree of the derivative of the dependent variable to differentiate first order from higher orders.

. A first order differential equation is the equation whose dependent variable derivative has a degree of one (i.e the highest degree of the derivative of the dependent variable in the differential equation is one). 

eg.

. Higher Orders, 

If the degree of the derivative of the dependent variable is two (i.e the highest degree of the derivative of the dependent variable is two) then it is a second order differential equation. 

If the degree of the derivative of the dependent variable is three (i.e the highest degree of the derivative of the dependent variable is three) then it is a third order differential equation.

The same goes with forth and other.

Eg

DE mean differential equation.