What are Differential Equations?
When an equation has one or more functions as well as its derivatives, it is known as a differential equation. There are certain terms that we need to take care of while studying differential equations. Those terms are given below:
2. Independent Variable: The dependent variable is dependent on another variable, which is known as the independent variable.
Note: The differential equations may or may not have either one or more than one dependent or independent variable.
Differential Equations have many use cases. They are taken into consideration almost in every field, be it chemistry, mathematics, biology, physics, engineering, and so on. From species of any living organism to rough engineering, chemical decomposition, population, and other areas of research, differential equations play a massive role.
The dependent variables, with consideration of independent variables, when forming a function derivative, then this phenomenon is known as differential equations.
Order and degree are the main terms that ought to be perceived while tackling the differential conditions. Order of a differential condition is the most noteworthy capacity to which the subordinates are brought up in the given condition. Be that as it may, degree then again is the force of the greatest subordinate. For instance, consider the differential condition referenced underneath.
(y’)2 + y’’’ - 2 (y’’)4 = 7y
The equation comprises the third derivative of 'y' as y''' which is the most noteworthy derivative. The power of y''' is 1. Thus, the level of the equation is '1'. Be that as it may, the subsequent derivative is y'' which is raised to power 4 which is the most elevated power of the derivative. Along these lines, the request for the given differential equation is 4.
The Different Types of Differential Equations
There are many different types of differential equations, starting with the basis of the type of variables, the types are:
Types of Differential Equations Based on the Order of Equations:
1. First order of differential equation: When 1 is the highest power of the formed derivatives.
2. Second-order of the differential equation: When 2 is the highest power of the formed derivatives.
3. N(th) order of differential equation: When 'N' is the highest power of the formed derivatives.
Types of differential equations based on homogeneity:
Homogenous differential equations
Non-homogeneous differential equations
Solution of Differential Equations:
Solving a differential equation means finding an equation that does not contain any derivatives. However, this equation should satisfy the differential equation that is being solved. Solving differential equations involves two or more integrations. To determine an appropriate method to solve the differential equation, it is very important to identify the type of differential equation that is being solved. Both general and particular solutions of differential equations can be obtained by using appropriate steps to solve the equation.
Fun facts:
A differential equation will generally have an infinite number of solutions.
A general formula can be derived for the solution of a few differential equations.
FAQs on Differential Equation And Its Types
1. What are the differential equations and what are the important terms in them?
The differential equation has one or more functions as well as its derivatives. There are certain terms that we need to take care of while studying differential equations. The important term is - Dependent Variable and Independent Variable. when an equation has only one variable, it is called a dependent variable, whereas the dependent variable is dependent on another variable, which is known as the independent variable.
2. What are the different types of differential equations?
There are many different types of differential equations, starting with the basis of the type of variables, the types are mentioned below -
- Partial Differential Equations:
When two or more two independent variables affect the dependent variable.
- Ordinary Differential Equations:
This generally depends on only one independent variable.
Types of differential equations based on the order of equations. First order of differential equation, Second-order of the differential equation, N(th) order of the differential equation.
3. Is there any use of differential equations in real life, if yes then explain?
Yes, there are numerous uses of differential equations in various sectors like maths, science, technology, and engineering, the differential equation is used to describe the exponential decay and growth of population and radioactive description, etc. the differential equations are also used to examine the return of investment and optimum investment strategies. Many physical quantities are calculate in physics are expressed in these equations.
4 . Is there any cases for a differential equation, explain?
Differential Equations have many use cases. The dependent variables, with consideration of independent variables, when forming a function derivative, then this phenomenon is known as differential equations. They are taken into consideration almost in every field, be it chemistry, mathematics, biology, physics, engineering, and so on. From species of any living organism to rough engineering, chemical decomposition, population, and other areas of research, differential equations play a massive role.
5 . What do you mean by solving a differential equation?
If any equation does not have any derivatives the solution of the respective equation is solving a differential equation. It is important that the respective equation should satisfy the differential equation. Two or more integrations are needed to satisfy and solve the differential equations. firstly, identify the type of differential equation that you are going to solve then use the appropriate method to solve it.
6. What is a differential equation? What are differential equation types?
Differential equations are equations that consist of functions along with their derivatives. Differential equations usually consist of derivatives of one variable called the dependent variable with respect to another variable called the independent variable. Differential equations are classified into several types based on various parameters.
Based on the type of variable used, they are classified as ordinary and partial differential equations.
Based on the order of differential equations, they are classified as first, second, third .. and nth order differential equations.
Linear and nonlinear differential equations
Homogeneous and nonhomogeneous differential equations
7. Where are differential equations used in real life?
Differential equations find an extensive range of applications in various domains of Science, Mathematics, Engineering and Technology. A few applications of differential equations include:
It is used to describe the functions which indicate the exponential growth and decay such as the growth of population and description of radioactive decay etc.
In economics, differential equations are used to describe the return of investment with respect to time and also optimum investment strategies.
In biology, especially in the field of medicine, differential equations are also used to describe the growth or spread of diseases such as cancer in the human body.
Several physical quantities in Physics can be expressed in terms of differential equations. Differential equations are also used to describe the motion of waves and particles.
