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Understanding Ordinary Differential Equations

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Understanding Ordinary Differential Equations

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Questions and Answers

What is an ordinary differential equation (ODE)?

A differential equation with no unknown function

A differential equation with no independent variable

A differential equation dependent on multiple independent variables

A differential equation dependent on a single independent variable (correct)

What type of differential equation is defined by a linear polynomial in the unknown function and its derivatives?

Linear differential equation (correct)

Quadratic differential equation

Trigonometric differential equation

Exponential differential equation

What are the arbitrary differentiable functions in a linear differential equation $a_0(x)y + a_1(x)y' + a_2(x)y'' + ⋯ + a_n(x)y^{(n)} + b(x) = 0$?

$b(x)$ only

$a_0(x)$ only

$a_0(x), a_1(x), ..., a_n(x)$ (correct)

$y, y', ..., y^{(n)}$

Why do linear differential equations play a prominent role among ordinary differential equations?

Most elementary and special functions encountered in physics and applied mathematics are solutions of linear differential equations Signup and view all the answers

What distinguishes ordinary differential equations from partial differential equations?

The number of independent variables they depend on Signup and view all the answers

What is the focus of Part A in the CSIR NET Mathematics exam?

General Paper common for all candidates Signup and view all the answers

Which topics are covered in Part A of the CSIR NET Mathematics Syllabus?

Partial differential equations, numerical analysis, calculus of variations Signup and view all the answers

In which parts of the CSIR NET Mathematics exam are the questions dependent on subject-specific choices made by the candidates?

Part B and Part C Signup and view all the answers

Which type of differential equation plays a prominent role in the CSIR NET Mathematics Syllabus?

Ordinary differential equations Signup and view all the answers

Why is a good understanding of the CSIR NET Mathematics Syllabus essential?

$To$ $crack$ $any$ $exam$ Signup and view all the answers