GATE MA topic:ordinary-differential-equations PYQs & Answers — Page 3

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topic:ordinary-differential-equations

Questions 21–30 of 51. Imported answers require independent review unless marked reviewed.

Topic practice 51 questionsPage 3 of 6

Consider the ordinary differential equation (ODE)

and

are the roots of the indicial equation of the above ODE at the regular singular point

, then

is equal to ________ (rounded off to 2 decimal places).

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The initial value problem

where

is a real constant, has

Your answerChoose one option.

a unique solution

exactly two solutions

infinitely many solutions

no solution

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If eigenfunctions corresponding to distinct eigenvalues

of the Sturm-Liouville problem

are orthogonal with respect to the weight function

, then

Your answerChoose one option.

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If the ordinary differential equation

has a solution of the form

, where

’s are constants and

, then the value of

is _____.

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The Bessel function

satisfy

. Then, the value of

is _____.

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Let

be an orthonormal set in

such that

, where

is a constant and

is the Legendre polynomial of degree

, for each

. Then, which of the following statements are TRUE?

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

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The eigenvalues of the boundary value problem

are given by

Your answerChoose one option.

, where

are the roots of

, where

are the roots of

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Let

be the solution of the following initial value problem

Then

__________.

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Let

be the solution of the initial value problem

obtained by the method of Laplace transform. Then

Your answerChoose one option.

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The critical point of the differential equation

is a

Your answerChoose one option.

node and is asymptotically stable

spiral point and is asymptotically stable

node and is unstable

saddle point and is unstable

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GATE MA topic:ordinary-differential-equations PYQs

Question 63

Question 19

Question 20

Question 33

Question 34

Question 52

Question 5

Question 20

Question 29

Question 30