GATE MA Ordinary Differential equations PYQs & Answers — Page 5

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Ordinary Differential equations

Questions 41–50 of 51. Imported answers require independent review unless marked reviewed.

Topic practice 51 questionsPage 5 of 6

The general solution of the differential equation

is given by (with an arbitrary positive constant

)

Your answerChoose one option.

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Let

be the polynomial solution of the differential equation

with

for

. If

then

Your answerChoose one option.

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If the Laplace transform of

is given by

, then

________.

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The number of regular singular points of the differential equation

in the interval

is equal to ________.

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Let

be a

matrix with real entries. If three solutions of the linear system of differential equations

are given by

then the sum of the diagonal entries of

is equal to _________.

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is a solution of the differential equation

for some real numbers

and

, then

_________.

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is an integrating factor of

, where

, then

Your answerChoose one option.

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and

are the solutions of the system

and

with the initial conditions

and

, then

equals ______.

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is the solution of the initial value problem

and

, where

, then

Your answerChoose one option.

and

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Let

and

for

. Consider the following statements: (P):

and

are linearly independent solutions of

. (Q): The Wronskian

for all

. Which of the above statements hold TRUE?

Your answerChoose one option.

Both P and Q

Only P

Only Q

Neither P nor Q

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GATE MA Ordinary Differential equations PYQs

Question 5

Question 6

Question 18

Question 19

Question 45

Question 46

Question 8

Question 9

Question 10

Question 35