GATE AE Differential Equations PYQs & Answers — Page 2

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Differential Equations

Questions 11–20 of 23. Imported answers require independent review unless marked reviewed.

Topic practice 23 questionsPage 2 of 3

Consider the differential equation

. The boundary conditions are

and

. Then the value of

Your answerChoose one option.

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Consider the partial differential equation

where

are real. If

, where

and

are real functions, which one of the following statements can be true?

Your answerChoose one option.

is a periodic function and

is a linear function

both

and

are exponential functions

is a periodic function and

is an exponential function

both

and

are periodic functions

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Consider the differential equation

and the boundary conditions

and

. The solution to this equation is:

Your answerChoose one option.

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is governed by the following equation

. The nature of this equation is:

Your answerChoose one option.

linear

elliptic

hyperbolic

parabolic

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, where

and

are constants, is a solution of

Your answerChoose one option.

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The similarity solution for the diffusion equation,

, where similarity variable,

. If

, the ratio

______ (round off to one decimal place).

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The equation

, where

is a constant, represents a family of

Your answerChoose one option.

exponential curves

parabolas

circles

hyperbolas

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The curve

is such that its slope is equal to

for all real

. If the curve passes through

, the value of

is ______ (round off to 1 decimal place).

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The solution of the differential equation

, given that

and

Your answerChoose one option.

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The eigenvalues

and eigenfunctions

of the Sturm-Liouville problem

are given by:

Your answerChoose one option.

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GATE AE Differential Equations PYQs

Question 37

Question 38

Question 1

Question 2

Question 3

Question 22

Question 26

Question 33

Question 26

Question 4