GATE MA Ordinary Differential equations PYQs & Answers — Page 4

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Ordinary Differential equations

Questions 31–40 of 51. Imported answers require independent review unless marked reviewed.

Topic practice 51 questionsPage 4 of 6

(

) is the power series solution of the differential equation

, then

__________.

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The initial value problem

has

Your answerChoose one option.

a unique solution if

no solution if

infinitely many solutions if

a unique solution if

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Let

be a solution of the differential equation

and let

be a solution of the differential equation

satisfying

and

. Then

Your answerChoose one option.

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For

, let

be a solution of the differential equation

satisfying

. For which of the following functions

, the integral

is equal to zero?

Your answerChoose one option.

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Suppose that

and

are linearly independent solutions of the differential equation

, and

. Then the smallest positive integer

such that

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Consider the boundary value problem (BVP)

with the boundary conditions

(

is a non-zero real number).

Then which one of the following statements is TRUE?

Your answerChoose one option.

For

, the BVP has infinitely many solutions

For

, the BVP has a unique solution

For

, the BVP has a solution

such that

for all

For

, the BVP has a solution

such that

for all

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Consider the differential equation

is the Laplace transform of

, then the value of

is ______ (round off to 2 places of decimal). (Here, the inverse trigonometric functions assume principal values only)

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Let

with

satisfy the Legendre differential equation

Then the value of

is equal to ______ (round off to 2 places of decimal).

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Consider the system of linear differential equations

with the initial conditions

. Then

is equal to _____.

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Consider the differential equation

The sum of the roots of the indicial equation of the Frobenius series solution for the above differential equation in a neighbourhood of

is equal to _____.

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GATE MA Ordinary Differential equations PYQs

Question 50

Question 3

Question 33

Question 34

Question 44

Question 39

Question 44

Question 49

Question 54

Question 55