GATE CE topic:differential-equations PYQs & Answers

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topic:differential-equations

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Questions 1–10 of 23. Imported answers require independent review unless marked reviewed.

Topic practice 23 questionsPage 1 of 3

An ordinary differential equation is given below.

Considering

and

as arbitrary constants, the general solution of the equation is

Your answerChoose one option.

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Consider differential equation

with the condition as y = 0 at x = 0. The value of y at x = 1.0 is ______ (rounded off to two decimal places).

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The “order” of the following ordinary differential equation is _____.

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Pick the CORRECT solution for the following differential equation

Your answerChoose one option.

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Let

be the solution of the initial value problem

, where

and

. Then,

is equal to ____________________ (rounded off to 1 decimal place).

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Consider two Ordinary Differential Equations (ODEs):

Which one of the following options is CORRECT?

Your answerChoose one option.

P is a homogeneous ODE and Q is an exact ODE.

P is a homogeneous ODE and Q is not an exact ODE.

P is a nonhomogeneous ODE and Q is an exact ODE.

P is a nonhomogeneous ODE and Q is not an exact ODE.

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tank of 3 m height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At

, an inflow of a salt solution of concentration 5 g/m

at the rate of 2 litres/s and an outflow of the well stirred mixture at the rate of 1 litre/s are initiated. This process can be modeled using the following differential equation:

where m is the mass (grams) of the salt at time t (seconds). The mass of the salt (in grams) in the tank at 75% of its capacity is __________ (rounded off to 2 decimal places).

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In the differential equation

is a positive constant. If

, and

, the value of

is _____________ (rounded off to three decimal places).

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The solution of the differential equation

is expressed as

, where

, and

are constants, with

and

being distinct and not equal to 2.5. Which of the following options is correct for the values of

and

Your answerChoose one option.

1 and 2

−1 and −2

2 and 3

−2 and −3

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For the equation

the correct description is

Your answerChoose one option.

an ordinary differential equation of order 3 and degree 2.

an ordinary differential equation of order 3 and degree 3.

an ordinary differential equation of order 2 and degree 3.

an ordinary differential equation of order 3 and degree 3/2.

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GATE CE topic:differential-equations PYQs

How to practice topic:differential-equations

Question 37

Question 46

Question 29

Question 36

Question 47

Question 15

Question 48

Question 30

Question 36

Question 12