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** What is Differential Equations **

A differential equation is an equation that contains one or more unknown functions and thier derivatives. The functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between these two.

The primary purpose of the differential equation is the study of solutions that satisfy the equations and the properties of the solutions. There are a lot of differential equations formulas to find the solution of the derivatives.

** Differential Equations Application **

The main purpose of the differential equation is for studying the solutions that satisfy the equations and the properties of the solutions. Differential equations are mainly used in the fields of physics, chemistry, biology, mathematics, economics, astronomy and engineering. Partial differential equations also play an important role in the theory of elasticity, hydraulics etc.

** Types of Differential Equations **

Differential equations can be divided into several types. All types related to differential equations and their applications are ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, linear and non-linear differential equations, homogeneous and non-homogeneous differential equation, functional differential equations and Original Differential Equation:.

** Ordinary differential equation (ODE)**

Ordinary differential equation (ODE), is an equation which consists of one or more functions of one independent variable along with their derivatives. The term ordinary is used in contrast with the term partial differential equation (PDE) is an equation which consists of more than one independent variable.

Ordinary differential equations arise in many different contexts including geometry, mechanics, astronomy and population modelling.

**Partial differential equation (PDE)**

Partial differential equation (PDE) is an equation which consists of more than one independent variable with their partial derivatives.

Ordinary differential equation (ODE) is form a subclass of partial differential equations which consists of one or more functions of one independent variable along with their derivatives.

Partial differential equations are use in mathematically-oriented scientific fields, such as physics and engineering. They are foundational in the modern scientific understanding of sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, fluid dynamics, elasticity, general relativity, and quantum mechanics (Schrodinger equation, Pauli equation, etc). They also arise from many purely mathematical considerations, such as differential geometry, they are the fundamental tool in the proof of the Poincaré conjecture from geometric topology.

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