What is Differential Equation?

Have you heard about the term derivatives? No! Let me tell you, derivatives are the change of a function per rate at a given point. Any equation containing one or more derivative functions is defined as the differential equation. There are different types of differential equations such as: the homogenous, the ordinal, the linear, the non-linear, etc. This equation is widely used in the field of physics, mathematics, biology, and various others. We can find the equation for it by using simple explicit formulas. In this article, we will try to cover basic concepts regarding differential equations such as their application, types, and detailed analysis.

Different Types of Differential Equation

As mentioned above, an equation containing one or more derivative functions is defined as the differential equation. There are various types of differential equations used in various calculations. The following points mentioned below analyses those types.

  • A type of differential equation that includes only one variable or one or more than one derivative with respect to variables is known as the ordinal equation of differentiation. It is also known as the ODE which is expressed as the variable which is independent. It is denoted by the letter ‘x’. The ordinal equation is categorized into two types: non-homogeneous and homogenous equations.
  • A homogeneous Equation is a type of ordinal differential equation where the degree of every variable is equal to each other.
  • A non-homogeneous equation is a type of ordinary differential equation where the degrees of every variable are not equivalent to each other.
  • A differential equation that involves only one derivative which is partial to more than one function with respect to one or more than one function is defined as the partial differential equation. It is also known as the PDE.

Applications of Differential Equation

Till now you may have got an overview of differential equations and it’s various types. In the mathematical and physical world, we see various applications of these equations. The following points mentioned below analyses the applications of it.

  1.  The differential equation is used to calculate the speed of a moving object, the motion of the object, or the sideways movement of a pendulum.
  2.  It is also used in the biological world as it is used to represent the growth of bacterias and diseases in a bar graph or coordinate graph.
  3. The equation is also helpful for the representation of radioactive decay in terms of a model.

What is Derivative Formula?

The process of calculating the change of function per rate at a given point is known as differentiation. The derivative formula helps us to calculate the change in the relationship between the two variables. The use of it ranges from finding the slope of a line that is curved and straight to finding the change in the value of measurement from the other measurement. You may find various terms related to derivative formulae such as the variable and exponent which is denoted by the help of letters of ‘x’ and ‘n’. The formula given for derivatives is extensively used in calculus and trigonometric identities.

Important Points

In this section, we will sum up the points that we have discussed in the topics mentioned above. The points are as follows.

  1.  The differential equation can be calculated using simple explicit formulas.
  2.  There are various types of differential formulas based on the variables and their degrees.
  3.  The equation of differentiation is used to find the derivative. Along with that, there are various applications you will find in the world of physics and biology.

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