GATE XE topic:ordinary-differential-equations PYQs & Answers

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topic:ordinary-differential-equations

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Questions 1–10 of 13. Imported answers require independent review unless marked reviewed.

Topic practice 13 questionsPage 1 of 2

Let

denote the Wronskian of two linearly independent solutions

and

of the differential equation

, then the value of

Your answerChoose one option.

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Let

be the solution of the initial value problem,

Then the value of

is equal to (Answer in integer)

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Let

be a non-zero quadratic polynomial satisfying the differential equation

where

is a real constant. If

, then the value of the integral

Your answerChoose one option.

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For some integer

, the differential equation

is transformed into

, where

and

. Then, the value of

is _____

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The second smallest eigenvalue of the eigenvalue problem

Your answerChoose one option.

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Let

and

be two linearly independent solutions of

Let

denote the Wronskian of

and

. If

then

is equal to ______.

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Let the transformation

reduce the ordinary differential equation

where

are real constants. Then, the arithmetic mean of

is ______ (round off to three decimal places).

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Let

be the solution of the initial value problem

If the plane curve parameterized by

having

-coordinate

and

-coordinate

is closed, then necessarily

Your answerChoose one option.

is a non-zero rational number.

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Let

and

be two linearly independent solutions of the differential equation

. If

, then

is ________ .

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The largest interval in which the initial value problem

has a unique solution is

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GATE XE topic:ordinary-differential-equations PYQs

How to practice topic:ordinary-differential-equations

Question 13

Question 16

Question 12

Question 16

Question 14

Question 15

Question 6

Question 3

Question 7

Question 1