GATE MA Ordinary Differential equations PYQs & Answers

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Ordinary Differential equations

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Questions 1–10 of 51. Imported answers require independent review unless marked reviewed.

Topic practice 51 questionsPage 1 of 6

Consider the following differential equation:

Which of the following statements is/are TRUE?

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

The point

is not a singular point.

The point

is a singular point.

The point

is a regular singular point.

The point

is not a regular singular point.

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The solution

of the initial value problem

is equal to

Your answerChoose one option.

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Let

be the unit impulse function defined by

when

and

. Consider the following initial value problem

with

and

. Which one of the following is TRUE?

Your answerChoose one option.

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Let

and

be the roots of the indicial equation obtained in the method of finding Frobenius series solution to the differential equation:

Which of the following statements is/are TRUE?

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

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Given that the Laplace transforms of

and

exist, where

is the Bessel function. Let

be the Laplace transform of the Bessel function

. Then, which one of the following is TRUE?

Your answerChoose one option.

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Consider the system of ordinary differential equations

where

is a

skew-symmetric matrix with entries in

. Then, for this system, the origin is a stable critical point for

Your answerChoose one option.

any such matrix

only such matrices

whose rank is 2

only such matrices

whose rank is 4

only such matrices

whose rank is 6

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Let

be the unique polynomial of degree

satisfying the Legendre differential equation

Then, the value of

is equal to _____ (in integer)

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Let

be the vector space (over

) consisting of all bounded real-valued solutions of the differential equation

Then, the dimension of

is _____ (in integer)

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Let

be the solution of the initial value problem

. Using Euler’s method, with the step-size

, the approximate value of

is equal to _____ (in integer)

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Let

be the solution of the differential equation

, satisfying

and

. Then, the value of

is equal to

Your answerChoose one option.

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GATE MA Ordinary Differential equations PYQs

How to practice Ordinary Differential equations

Question 27

Question 36

Question 40

Question 51

Question 12

Question 16

Question 28

Question 31

Question 35

Question 37