GATE MA topic:ordinary-differential-equations PYQs & Answers — Page 2

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topic:ordinary-differential-equations

Questions 11–20 of 51. Imported answers require independent review unless marked reviewed.

Topic practice 51 questionsPage 2 of 6

Let

and

be the two linearly independent solutions of the differential equation

, satisfying the initial conditions

and

. Define

. Then, the value of

Your answerChoose one option.

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and

are two different solutions of the ordinary differential equation

then which one of the following is its general solution on

Your answerChoose one option.

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Consider the initial value problem (IVP)

I. IVP has a unique solution on

II. Every solution of IVP is bounded on its maximal interval of existence.

Which one of the following is correct?

Your answerChoose one option.

Both I and II are TRUE

I is TRUE and II is FALSE

I is FALSE and II is TRUE

Both I and II are FALSE

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Let

be a

non-diagonalizable real matrix with a real eigenvalue

and

be an eigenvector of

corresponding to

. Which one of the following is the general solution of the system

of first-order linear differential equations?

Your answerChoose one option.

, where

and

is a

real column vector such that

, where

and

is a

real column vector such that

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Which of the following is/are eigenvalue(s) of the Sturm–Liouville problem

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

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The boundary value problem

has infinitely many distinct solutions when

is equal to

(round off to TWO decimal places)

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Let

be the solution of the initial value problem

, then the value of

is ______ (rounded off to 2 decimal places).

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Let

and

be two linearly independent solutions of the ordinary differential equation

Let

be such that

and

for all

. Consider the following statements:

for all

Then

Your answerChoose one option.

is TRUE and

is FALSE

is FALSE and

is TRUE

both

and

are FALSE

both

and

are TRUE

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Let

, be two functions satisfying the following system of differential equations:

and

, where

are real numbers.

Which of the following statements is/are correct?

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

, then

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For every

, let

be a polynomial of degree

with

. Further, let

satisfy the Legendre equation

for some positive integer

, then the value of

is ____________.

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GATE MA topic:ordinary-differential-equations PYQs

Question 38

Question 24

Question 44

Question 45

Question 53

Question 63

Question 33

Question 41

Question 49

Question 62