Ordinary Differential Equation

By : Ashish Rawat

Updated : Feb 18, 2021, 6:54

The ordinary differential equation is a mathematical tool used to evaluate the relationship between independent variables with derivatives. And the same abbreviate as ODE. y’=x+1 is an instance of ODE. Ordinary differential equation (ODE) MCQs form an essential quotient for most competitive exams nationwide. The ordinary differential equation (ODE) GATE questions span across all its various categories, comprising GATE ECE, GATE CSE, GATE Civil, GATE Mechanical, and GATE Electrical.

Important Ordinary Differential Equation topics for GATE CE

Ordinary differential equations is one of the essential concepts used in a wide variety of math and science classes and engineering, astronomy, and other fields that require a lot of straight-line/plane surfaces. The ordinary differential equation (ODE) GATE syllabus comprises the following essential topics held in the ordinary differential equation (ODE) quiz:

Topic	Explanation
Integral Equation	It is very useful when solving a system of ODE. It also solves any one-step integral structure, such as the Navier-Stokes (NPS) form in Cartesian and integral calculus. Other uses include solving quadratic equations, the system of complex numbers, and the binomial coefficient.
Algebraic equation	It is one of the four types of equations in algebra, which can be solved algebraically. The solutions of these equations form the basis for many other equations in algebra, including those concerning the plane, sphere, closed-form and non-labelled (convergence) functions.
Single Variable Duality	It is a concept that has been developed to provide a simpler and easier way of solving problems related to high degree solutions (ordinary singular derivatives) in ODE, Dynamics, or numerical analysis. It is also known as 'singular integral' since it does not require the use of a product of two variables.
Numerical Analysis and Solving	Ordinary differential equations are necessary to formulate many critical scientific processes and aid in numerical analysis and solve the same central concept as all the derivatives equal to the root. And hence the sum of the derivatives is zero.

Tips for Solving Ordinary Differential Equation Questions in GATE Exam

There are many useful tips for solving ordinary differential equation (ODE) online test, and ordinary differential equation (ODE) online quiz:

You can quickly solve by taking all the terms of x on one side and all the words of y on another side and then integrating both sides.
With the aid of standard variable separable methods, you can obtain the answer for ODE problems.
While solving the ordinary differential equation, it involves ‘integration’ at some point. And for the same, you should end up with an expression along the lines of “y = ...”.

Importance of Ordinary Differential Equation (ODE) Syllabus for GATE

Ordinary differential equation (ODE) for GATE CE holds the following importance.

ODE questions test the students’ knowledge in basic concepts like algebra, geometry, calculus etc.
This kind of exam makes the students think seriously about the questions and answer the queries correctly.
By developing Ordinary Differential Equations’ concepts, the students can derive the equations of motion, displacement, and acceleration.
It can be done by developing a model in which the motion is performed, the characteristics of the model can be analyzed, the derivative of the function is explored, and the solutions of the equations of motion, acceleration, and displacement.

Most Recommended Ordinary Differential Equation Books for GATE

The following ordinary differential equation (ODE) books cover all the topics, a part of the ordinary differential equation (ODE) syllabus for GATE. They help in easy preparation with ordinary differential equation (ODE) study material for GATE CE.

Book	Author
Theory of Ordinary Differential Equations	Christopher P. Grant
An Introduction to Ordinary Differential Equations	Earl A. Coddington
Differential Equations with Applications and Historical Notes	Simmons George
Essentials of Ordinary Differential Equations Paperback	Ravi P. Agarwal

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Indeed, you cannot expect to solve all the problems if you do not understand all ‘differential equations’ concepts. Here is where the idea of learning from Gradeup comes in. There are several concerning ordinary differential equation (ODE) notes for CE, ordinary differential equation (ODE) notes for GATE PDF along with its preparation after joining BYJU'S Exam Prep –

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FAQs

Q. Define the order of ODE.

ODE’s order defines the order of the highest derivative occurring in the equation.

Q. What is the full form of ODE?

ODE stands for Ordinary Differential Equation.

Q. What are the types of ordinary differential equations?

Autonomous Ordinary Differential Equations
Linear Ordinary Differential Equations
Non-linear Ordinary Differential Equations

Q. Explain an explicit ordinary differential equation.

With x as an independent variable, y as a dependent variable and F as a function of both x, y and derivatives of variable y, ODE’s explicit order is provided by the equation: F(x, y, y’, …., yn-1) = yn.

Q. What is the use of ordinary differential equations?

ODE’s application helps model the upheaval of various diseases, demonstrating the pendulum’s motion and electricity movements.