GATE ES topic:differential-equations PYQs & Answers

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Questions 1–10 of 12. Imported answers require independent review unless marked reviewed.

Topic practice 12 questionsPage 1 of 2

A first-order ordinary differential equation is given as follows:

Which ONE of the following options CORRECTLY represents the characteristics of this equation?

Your answerChoose one option.

Linear, homogeneous, and exact

Nonlinear, nonhomogeneous, and exact

Linear, homogeneous, and non-exact

Nonlinear, nonhomogeneous, and non-exact

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Assuming

; Laplace transform of

Your answerChoose one option.

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For the ordinary differential equation

, the general solution is

Your answerChoose one option.

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A tank has inflow, outflow and stirring mechanism. Initially, the tank holds 500 L of a brine solution of concentration 200 g/L. At

, an inflow of another brine solution of concentration 100 g/L starts entering the tank at the rate of 15 L/minute. At the same time the outflow of thoroughly stirred mixture also takes place at the same rate so that the volume of brine in the tank remains constant. The brine concentration

(g/L) in the tank at any time

(minute) can be expressed by the following differential equation

The brine concentration in the tank at

hour is ________ g/L. (rounded off to two decimal places)

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Consider the equation

; with y = 1 at x = 0.

The value of y at x = 1 is ______ (rounded off to 2 decimal places).

Take the value of e (base of natural logarithm) as 2.7.

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Which one is the solution y(x) for the following ordinary differential equation and the specified boundary conditions?

Your answerChoose one option.

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Given are two ordinary differential equations

The correct choice is

Your answerChoose one option.

P is linear; Q is nonlinear

P is nonlinear; Q is linear

Both P and Q are linear

Both P and Q are nonlinear

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Second order ordinary differential equation

has values

and

. The value of y at x=1 is __________________ (rounded off to three decimal places).

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Assuming

; Laplace transform for

Your answerChoose one option.

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Given,

;

. The problem is a/an

Your answerChoose one option.

initial value problem having solution

boundary value problem having solution

initial value problem having solution

boundary value problem having solution

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GATE ES topic:differential-equations PYQs

How to practice topic:differential-equations

Question 36

Question 11

Question 12

Question 50

Question 33

Question 37

Question 11

Question 47

Question 13

Question 36