Engineering Maths · all questions

Differential Equations
practice.

Practice every MCQ with options. Use Show answers when you want the correct option and solution.

Questions

3/5

Page

Pick an option on a question to see the right answer and solution.

Q41

Open question

Solution of

\frac{dy}{dx} = - \frac{x}{y}

at x = 1 and y = √3 is

Select an option to see the answer and solution.

Q42

Open question

The solution to the ordinary differential equation

\frac{d ^{2} y}{d x ^{2}} + \frac{dy}{dx} - 6 y = 0

Select an option to see the answer and solution.

Q43

Open question

Consider the differential equation

\frac{dy}{dx} = 1 + y^{2} .

Which one of the following can be a particular solution of this differential equation?

Select an option to see the answer and solution.

Q44

Open question

Which ONE of the following is a linear non-homogeneous differential equation, where x and y are the independent and dependent variables respectively?

Select an option to see the answer and solution.

Q45

Open question

A body originally at 60°C cools down to 40°C in 15 minutes when kept in air at a temperature of 25°C. What will be the temperature of the body at the end of 30 minutes?

Select an option to see the answer and solution.

Q46

Open question

The figure shows the plot of y as a function of x
Differential Equations mcq question image

The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is

Select an option to see the answer and solution.

Q47

Open question

The following differential equation has

3 (\frac{d ^{2} y}{d t ^{2}}) + 4 (\frac{dy}{dt})^{3} + y^{2} + 2 = x

Select an option to see the answer and solution.

Q48

Open question

The boundary-value problem y'' + λy = 0, y(0) = y(π) = 0 will have non-zero solutions if and only if the values of λ are

Select an option to see the answer and solution.

Q49

Open question

The general solution of the differential equation

\frac{dy}{dx} = \frac{1 + cos 2 y}{1 - cos 2 x}

Select an option to see the answer and solution.

Q50

Open question

The solution of the differential equation

\frac{dy}{dx} + 2 xy = e^{- x^{2}}

with y(0) = 1 is

Select an option to see the answer and solution.

Q51

Open question

The solution of

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{dy}{dx} + 17 y = 0;

y(0) = 1,

\frac{dy}{dx} (\frac{π}{4}) = 0

in the range 0 < x <

\frac{π}{4}

is given by

Select an option to see the answer and solution.

Q52

Open question

The differential equation

\frac{d ^{2} y}{d x ^{2}} + 16 y = 0

for y(x) with the two boundary conditions

\frac{dy}{dx}_{x = 0} = 1

and

\frac{dy}{dx}_{x = \frac{π}{2}} = - 1

has

Select an option to see the answer and solution.

Q53

Open question

The solution of the differential equation

x^{2} \frac{d ^{2} y}{d x ^{2}} - x \frac{dy}{dx} + y = lo g x

Select an option to see the answer and solution.

Q54

Open question

Solution of the differential equation

3 y \frac{dy}{dx} + 2 x = 0

represents a family of

Select an option to see the answer and solution.

Q55

Open question

The solution of differential equation

\frac{dy}{dx} - y^{2} = 1

satisfying condition y = 0 is

Select an option to see the answer and solution.

Q56

Open question

The solution of the initial value problem

\frac{dy}{dx} = - 2 xy;

y(0) = 2 is

Select an option to see the answer and solution.

Q57

Open question

An ordinary differential equation is given below.

(\frac{dy}{dx}) (x ln x) = y

The solution for the above equation is
(Note: K denotes a constant in the options)

Select an option to see the answer and solution.

Q58

Open question

The solution to the differential equation

\frac{d ^{2} \cdot u}{d x ^{2}} - k \frac{du}{dx} = 0

is where k is constant, subjected to the boundary conditions u(0) = 0 and u(L) = U, is

Select an option to see the answer and solution.

Q59

Open question

The matrix form of the linear system

\frac{dx}{dt} = 3 x - 5 y

and

\frac{dy}{dt} = 4 x + 8 y

Select an option to see the answer and solution.

Q60

Open question

The solution of the equation

\frac{dQ}{dt} + Q = 1

with Q = 0 at t = 0 is

Select an option to see the answer and solution.

Prev 1 2 3 4 5 Next

Differential Equationspractice.

Differential Equations
practice.