Differential Equations are equations with a function and more than one of its derivatives For example: dy/dx + 5y = 7x, where y is the function and dy/dx is the derivative. Differential Equations are mainly used in the field of physics, as derivatives define the rate of change of a function at a given point of time. Differential Equations are equations that summarise a relationship between a quantity that is changing with respect to some other quantity or variable. This article will help you prepare for GATE by providing Differential Equations tips and tricks for GATE, Differential Equations GATE ECE questions and answers pdf, names of Differential Equations books to study from, Differential Equations notes for GATE pdf, Differential Equations topics for GATE ECE, and Differential Equations syllabus for GATE.
Important Differential Equations Terminology
Order of Differential Equations
Order is the power or order of the highest power derivative in the given equation. For example: dy/dx+x = 3, here the order is 1, as the highest order derivative is dy/dx and its order is 1.
First-order Differential Equations
First-order Differential Equations are equations that have an order equal to 1 like all linear Differential Equations. The first-order derivative is in the form of dy/dx. It is represented as y'.
Second-order Differential Equations
Second-order Differential Equations are equations that have an order equal to 2. There exists a second-order derivative in the form of d2y/dx2. It is represented as y".
Ordinary Differential Equations
Ordinary Differential Equations are equations that contain only one independent variable and its derivative.
Partial Differential Equations
Partial Differential Equations are equations which contain more than one independent variable and its partial derivative. It is a special form of ordinary Differential Equations.
Linear Differential Equations
It is a linear equation that consists of a derivative of anyone variable with respect to other independent variables. It is usually the first-order Differential Equation. For example: dx/dy+7x = 5.
Homogeneous Differential Equations
Differential variables in the form of f(x,y)dy = g(x,y)dx, where f and g are the same functions of x and y. It is solved using the separation of variables technique and integration.
Separation of variable method
It is a method of solving Differential Equations which can be expressed in the form of dy/dx = f(y)g(x). It involves re-writing the equation as 1/f(y)dy = g(x)dx and then applying integration to both sides.
Integrating factor method
It is the second method of solving Differential Equations which can be expressed in the form of dy/dx+p(x)y = q(x), where p and q are the functions of variable x.
Tips to Solve Differential Equation Questions for GATE ECE
- To understand Differential Equations properly, you must understand what differentiation, integration, and continuity are.
- First, try understanding the basic concepts and topics of Differential Equations.
- Always practice from NCERT and RD Sharma of Class 12th as it helps to build your base and a lot of questions are directly from these books.
- Practice mock tests and previous year examinations as it will help you judge the difficulty level and then prepare accordingly.
Importance of Differential Equations in GATE ECE
- Differential Equations are an important part of Mathematics and competitive examinations. Every year, these examinations contain questions from Differential Equations.
- Every year the weightage of differential equations in GATE examination is one of the highest. So, practicing it is really important to score well.
- Every year JEE and GATE examinations include questions from Differential Equations, calculus, and derivatives. There are at least 2 - 3 questions from each of these topics.
- Almost all major engineering exams have differential equation questions.
Recommended Books for Differential Equations
There are many books to prepare Differential Equations for GATE examinations, but it is always advisable to finish NCERT first. These Differential Equations books help you with Differential Equations study material for GATE ECE and Differential Equations MCQ pdf.
Mathematics Class 12th
Integral Calculus and Differential Calculus
Differential Equations for Dummies
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Frequently Asked Questions (FAQs)
Ques. What is the weightage of differential equations in competitive examinations?
On average, around 2-3 questions are asked from differential equations and its sub-topics in competitive examinations.
Ques. Which examinations include questions from differential equations?
Every examination which has a mathematical section includes questions from differential equations. Following are a few examinations:
- GATE ECE and other disciplines
- CAT, MAT, XAT, and other MBA exams
Ques. What are the uses of differential equations?
It is used to express the change of one variable with respect to other variables. It is used in biology to study growth and decay over a period of time. It is used in economics to express the growth and fall of an economy.
Ques. How are differential equation questions asked in examinations?
They are asked in the form of MCQs in competitive examinations. No subjective questions are asked.
Ques. Do college entrance examinations include questions from differential equations?
Yes, a lot of college entrance examinations. If you are preparing for any undergraduate or postgraduate college examination, then study differential equations properly.