Elementary Differential Equations

A differential equation is a mathematical equation for an unknown function of one or more variables that correlates the values of the function and its derivatives of several orders. It plays an important role in economics, engineering and many other fields. .

How to study Differential Equations:

They are mathematically studied from various different views, mostly connected with their inferences-the set of functions that satisfy the equation. If there's no self-contained formula for the inference, the inference may be numerically approximated using systems.

The theory of differential equations is well developed and the procedures used to infer them vary significantly with equation type. They are as follows:

• Ordinary Differential Equations (ODE): This is a equation in which the unknown function (otherwise known as dependent variable) is a function of an individual independent variable. This also consists of 2 types of equations based on the order, namely,
  • First order differential equation
  • Second order differential equation
  • Nth order differential equation or Higher order differential equation
• Partial Differential Function (PDF): This is a equation in which the unknown function is a function of several independent variables and it involves its own partial derivatives. The equations taken into consideration are:
  • The Heat Equation
  • The Wave Equation

Both PDF and ODE are mainly divided as linear and non-linear. Therefore, the equation is linear if the function not known and its derivatives appear to the power 1 and non-linear otherwise. Non-Linear differential equations can be explicitly solved using very few procedures whereas linear differential equations frequently appear as approximations to non-linear equations.

Summary:

Three types of equations are related to the differential equations. They are namely; delay differential equations (DDE), stochastic differential equations (SDE) and differential algebraic equation (DAE). This equation is also closely related to the difference equation theory.