Sorry, you have Javascript Disabled! To see this page as it is meant to appear, please enable your Javascript!

MISCELLANEOUS QUIZ ON DIFFERENTIAL EQUATION

MISCELLANEOUS QUIZ ON DIFFERENTIAL EQUATION

Time limit: 0

Quiz Summary

0 of 10 questions completed

Questions:

1
2
3
4
5
6
7
8
9
10

Information

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading…

You must sign in or sign up to start the quiz.

You must first complete the following:

Results

Quiz complete. Results are being recorded.

Results

0 of 10 questions answered correctly

Your time:

Time has elapsed

You have reached 0 of 0 point(s), (0)

Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)

Categories

MISCELLANEOUS QUIZ ON DIFFERENTIAL EQUATION 0%

1
2
3
4
5
6
7
8
9
10

Answered
Review

Question 1 of 10

1. Question
The solution of $\dfrac{{{d^2}y}}{{d{x^2}}} - y = 1,$ which vanish when x = 0 and tends to a finite limit as $x \to - \infty$
- $y = e^x - 1$
- $y = e^x + 1$
- $y = e^{-x} - 1$
- $y = e^{-x} + 1$
Correct

Incorrect
Question 2 of 10

2. Question
The second order linear differential with constant coefficients that has y₁ = e^–^xcos4x and y₂ = e^–^xsin4x as the solution
- $\dfrac{{{d^2}y}}{{d{x^2}}} - 2\dfrac{{dy}}{{dx}} + 17y = 0$
- $\dfrac{{{d^2}y}}{{d{x^2}}} + 2\dfrac{{dy}}{{dx}} + 17y = 0$
- $\dfrac{{{d^2}y}}{{d{x^2}}} + 2\dfrac{{dy}}{{dx}} - 17y = 0$
- $\dfrac{{{d^2}y}}{{d{x^2}}} + \dfrac{{dy}}{{dx}} - 17y = 0$
Correct

Incorrect
Question 3 of 10

3. Question
Find the intervals on which the differential equation is normal (1 – x²)y” – 2xy‘ + n(n + 1)y = 0, n is an integer
- $\left( { - \infty , - 1} \right)$
- (–1, 1)
- $\left( { - 1,\infty } \right)$
- $\left({ - \infty ,\infty} \right)$
Correct

Incorrect
Question 4 of 10

4. Question
The solution of (D + 1)x + (D – 1)y = e^t and (D² + D + 1)x + (D² – D + 1)y = x² is
- $x = \dfrac{1}{2}{e^{ - t}} + \dfrac{1}{2}{t^2} - t,\;\;y = \dfrac{1}{2}{t^2} + t - \dfrac{3}{2}{e^{ - t}}$
- $x = \dfrac{1}{2}{e^t} - \dfrac{1}{2}{t^2} + t,\;\;y = \dfrac{1}{2}{t^2} + t - \dfrac{3}{2}{e^t}$
- $x = - \dfrac{1}{2}{e^t} + \dfrac{1}{2}{t^2} - t,\;\;y = - \dfrac{1}{2}{t^2} - t + \dfrac{3}{2}{e^t}$
- $x = - \dfrac{1}{2}{e^t} + \dfrac{1}{2}{t^2} + t,\;\;y = \dfrac{1}{2}{t^2} - t - \dfrac{3}{2}{e^{ - t}}$
Correct

Incorrect
Question 5 of 10

5. Question
The number of arbitrary constants involved in the solution of
(D + 1)x + (D – 1)y = e^t
(D² + D + 1)x + (D² – D + 1)y = t² are
- 1
- 2
- 0
- 3
Correct

Incorrect
Question 6 of 10

6. Question
Let y = f(x) be twice continously differentiation function on $\left( {0,\infty } \right)$ satisfying f(1) = 1 and $f'(x) = \dfrac{1}{2}f\left( {\dfrac{1}{x}} \right),x > 0$ . What is the value of f (4)
- 2
- 0
- $\sqrt 2$
- 4
Correct

Incorrect
Question 7 of 10

7. Question
If y₁ = e²^x and y₂ = xe²^x, then P(0) is
- @@wpProQuizCloze-0@@
Correct

Incorrect
Question 8 of 10

8. Question
The orthogonal trajectory of family cardiods $r = a\left( {1 + \cos \theta } \right)$ is the family of
- Astroids
- Cardiods
- Cycloids
- ellipses
Correct

Incorrect
Question 9 of 10

9. Question
The set of linearly independent solution of differential equation $\dfrac{{{d^4}y}}{{d{x^4}}}(x) - \dfrac{{{d^2}y}}{{d{x^2}}} = 0$ is
- ${1, x, e, e^{-x}}$
- ${1, x, e^{-x}, xe^{-x}}$
- ${1, x, ex, xe^x}$
- ${1, x, e^x, xe^{-x}}$
Correct

Incorrect
Question 10 of 10

10. Question
The solution of $2{x^2}y\dfrac{{{d^2}y}}{{d{x^2}}} + 4{y^2} = {x^2}{\left( {\dfrac{{dy}}{{dx}}} \right)^2} + 2xy\dfrac{{dy}}{{dx}}$
- $y = x^3(c_1 + c_2 \rm log x)$
- $y = x(c_1 + c_2 \rm log x)^2$
- $y = x^{-1}(c_1 + c_2 \rm log x)^2$
- $y = x^2(c_1 + c_2 \rm log x)^2$
Correct

Incorrect

Log In ×

Email/Mobile Number

Password

Captcha

OTP

Remember Me

Forgot your Password?

Login With OTP

Resend OTP(00:30)

Don't have an account?

Signup

Email/Mobile Number

OTP

Password

Confirm Password

Resend OTP(00:30)

Back to login

Mobile Number

Mobile Number

OTP *

OTP

Resend OTP (00:30)

Back to login

Login

Accessing this course requires a login. Please enter your credentials below!

Username or Email Address

Password

Remember Me

Lost Your Password?

Register

Don't have an account? Register one!

Register an Account

Username

Email

Mobile Number

OTP *

Registration confirmation will be emailed to you.