GATE ECE Differential Equations PYQs & Answers

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Questions 1–10 of 14. Imported answers require independent review unless marked reviewed.

Topic practice 14 questionsPage 1 of 2

Consider the differential equation

, with

. If

be the solution to the equation where

and

are unit vectors along the positive x and y axes respectively, then which of the following options is the correct matrix representing A?

Your answerChoose one option.

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The function

satisfies

where

and

denote the first and second derivatives of

, respectively.

Given

and

, the maximum value of

over

is _____ (rounded off to two decimal places).

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The general form of the complementary function of a differential equation is given by

, where A and B are real constants determined by the initial condition. The corresponding differential equation is _____.

Your answerChoose one option.

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Consider the following partial differential equation (PDE)

where

and

are distinct positive real numbers. Select the combination(s) of values of the real parameters

and

such that

is a solution of the given PDE.

Your answerSelect all correct options. You can choose more than one.

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Consider the following wave equation,

Which of the given options is/are solution(s) to the given wave equation?

Your answerSelect all correct options. You can choose more than one.

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Consider the differential equation given below.

The integrating factor of the differential equation is

Your answerChoose one option.

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The general solution of

Your answerChoose one option.

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Which one of the following options contains two solutions of the differential equation

Your answerChoose one option.

and

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The families of curves represented by the solution of the equation

for

and

, respectively, are

Your answerChoose one option.

Paramas and Circles

Circles and Hyperbolas

Hyperbolas and Circles

Hyperbolas and Parabolas

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Consider the homogeneous ordinary differential equation

, with

as a general solution. Given that

and

, the value of

, rounded off to two decimal places, is ______.

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GATE ECE Differential Equations PYQs

How to practice Differential Equations

Question 11

Question 32

Question 11

Question 25

Question 30

Question 2

Question 4

Question 27

Question 2

Question 43