Ordinary Differential Equations Multiple Choice Questions and Answers - Sanfoundry PDF

Preview

Summary

mcqs...

Description

3/31/2021

Ordinary Differential Equations Multiple Choice Questions and Answers - Sanfoundry



Ordinary Dierential Equations Questions and Answers – Solution of DE With Constant Coecients using the Laplace Transform « Prev

Next »

This set of Ordinary Dierential Equations Multiple Choice Questions & Answers focuses on “Solution of DE With Constant Coecients using the Laplace Transform”. 1. While solving the ordinary dierential equation using unilateral laplace transform, we consider the initial conditions of the system. b) False View Answer Answer: a Explanation: When bilateral laplace transformation is used in solving dierential equations,

https://www.sanfoundry.com/ordinary-differential-equations-multiple-choice-questions-answers/



1/7

3/31/2021

Ordinary Differential Equations Multiple Choice Questions and Answers - Sanfoundry

advertisement

2. With the help of _____________________ a) Theory of calculus

.

b) Theory of probability c) Theory of statistics d) View Answer Answer: d Explanation: Let f(t) be the function in time. The laplace transformation of the function is L[f(t)] = F(s). So, the inverse laplace transform of F(s) comes out to be the function f(t) in time. The formula for laplace transform is derived using the theory of residues by Mr.Melin. 3. What is a) sy(0) – Y(s)

y(t) with respect to t : y’(t)?

c) s2 Y(s)-sy(0)-y'(0) 2

d) s Y(s)-sy'(0)-y(0) View Answer Answer: b Explanation: Let \(f(t) = y(t) \) \(L[f’(t)] = \int_0^∞ e^{-st} f'(t)dt \)

https://www.sanfoundry.com/ordinary-differential-equations-multiple-choice-questions-answers/



2/7

3/31/2021

Ordinary Differential Equations Multiple Choice Questions and Answers - Sanfoundry

4. Solve the Ordinary Dierential Equation by Laplace Transformation y’’ – 2y’ – 8y = 0 if y(0) = 3 and y’(0) = 6. a) \(3e^t cos(3t)+tsint(3t) \) b) \(3e^t cos(3t)+te^{-t} sint(3t) \) c) \(2e^{-t} cos(3t)-2 \frac{t}{3} sint(3t) \) d) \(2e^{-t} cos(3t)-2 \frac{te^{-t}}{3} sint(3t) \) View Answer Answer: a Explanation: L[y’’ – 2y’ – 8y ] = 0 2

s Y(s) – sy(0) – y'(0) – 2sY(s) + 2y(0) – 8Y(s) = 0 2 (s – 2s – 8)Y(s) = 2s \(L[y(t)] = 2 \frac{s}{(s^2-2s-8)} \) t Therefore, y(t) = 3e cos(3t) + tsint(3t). -t

5. Solve the Ordinary Dierential Equation y’’ + 2y’ + 5y = e sin(t) when y(0) = 0 and y’(0) = 1.(Without solving for the constants we get in the partial fractions). a) \(e^t [Acost+A1sint+Bcos(2t)+\frac{(B1)}{2} sin(2t)] \) b) \(e^{-t} [Acost+A1sint+Bcos(2t)+B1sin(2t)] \) c) \(e^{-t} [Acost+A1sint+Bcos(2t)+\frac{(B1)}{2} sin(2t)] \) d) \(e^t [Acost+A1sint+Bcos(2t)+(B1)sin(2t)] \) View Answer Answer: c Explanation: \(L[y’’+2y’ +5y = e^{-t} sin(t)] \) \(s^2 Y(s)-sy(0)-y'(0)+ 2sY(s) -2y(0) + 5Y(s) = \frac{1}{(s+1)^2+1} \) \((s^2+2s+5)Y(s)= \frac{1}{(s+1)^2+1}+1 \) \((s^2+2s+5)Y(s)= \frac{(s^2+2s+3)}{(s^2+2s+2)} \) \( Y(s) = \frac{(s^2+2s+3)}{(s^2+2s+2)(s^2+2s+5)} \) \( = \frac{(s+1)^2+2}{((s+1)^2+1)((s+1)^2+4)} \) \( y(t) = e^{-t} L^{-1} [\frac{(As+A1)}{(s^2+1)}+\frac{(Bs+B1)}{(s^2+4)}] \) \( = e^{-t} [Acost+A1sint+Bcos(2t)+\frac{(B1)}{2} sin(2t)]\). advertisement



https://www.sanfoundry.com/ordinary-differential-equations-multiple-choice-questions-answers/

3/7

3/31/2021

Ordinary Differential Equations Multiple Choice Questions and Answers - Sanfoundry

6. Solve the Ordinary Diferential Equation using Laplace Transformation y’’’ – 3y’’ + 3y’ – y = t2 et when y(0) = 1, y’(0) = 0 and y’’(0) = 2. a) \(2e^t \frac{t^5}{720}+e^t+2e^t \frac{t}{6}+4e^t \frac{t^2}{24} \) b) \(e^t \frac{t^5}{720}+2e^{-t}+2e^t \frac{t}{6}+4e^t \frac{t^2}{24} \) c) \(e^{-t} \frac{t^5}{720}+e^{-t}+2e^{-t} \frac{t}{6}+4e^{-t} \frac{t^2}{24} \) d) \(2e^{-t} \frac{t^5}{720}+e^{-t}+2e^{-t} \frac{t}{6}+4e^{-t} \frac{t^2}{24} \) View Answer 2

t

7. Take Laplace Transformation on the Ordinary Dierential Equation if y’’’ – 3y’’ + 3y’ – y = t e if y(0) = 1, y’(0) = b and y’’(0) = c. a) \((s^3-3s^2+3s-1)Y(s)+(-as^2+(3a-b)s+(-3a-c))=\frac{2}{(s-1)^3} \) b) \((s^3-3s^2+3s-1)Y(s)+(-as^2+(3a-b)+(-3a-c)s)=\frac{2}{(s-1)^3} \) c) \((s^3-3s^2+3s)Y(s)+(-as+(3a-b)s+(-3a-c))=\frac{2}{(s-1)^3} \) d) \((s^3-3s^2+3s-1)Y(s)+(-as^2+(3a-b)s+(-3a-c))=\frac{2}{(s-1)^3} \) View Answer 8. What is the inverse Laplace Transform of a function y(t) if after solving the Ordinary Dierential Equation Y(s) comes out to be \(Y(s) = \frac{s^2-s+3}{(s+1)(s+2)(s+3)} \) ? a) \(\frac{1}{2} e^{-t}+\frac{9}{2} e^{-3t}-3e^{-2t} \) b) \(\frac{-1}{2} e^{-t}+\frac{9}{2} e^{-2t}-3e^{-3t} \) c) \(\frac{1}{2} e^{-t}-\frac{3}{2} e^{-2t}-3e^{-3t} \) d) \(\frac{-1}{2} e^{t}+\frac{9}{2} e^{2t}-3e^{3t} \) View Answer 9. For the Transient analysis of a circuit with capacitors, inductors, resistors, we use bilateral Laplace Transformation to solve the equation obtained from the Kircho’s current/voltage law. a) True b) False View Answer Answer: b

https://www.sanfoundry.com/ordinary-differential-equations-multiple-choice-questions-answers/



4/7

3/31/2021

Ordinary Differential Equations Multiple Choice Questions and Answers - Sanfoundry

advertisement

10. While solving an Ordinary Dierential Equation using the unilateral Laplace Transform, it is possible to solve if there is no function in the right hand side of the equation in standard form and . a) True

View Answer Answer: b Explanation: It is not possible to solve an equation if the input and the initial conditions are zero becase Y(s) becomes zero where Y(s) is the Laplace Transform of y(t) function. Sanfoundry Global Education & Learning Series – Ordinary Dierential Equations. To practice all areas of Ordinary Dierential Equations, here is complete set of 1000+ Multiple Choice Questions and Answers. Participate in the Sanfoundry Certication contest to get free Certicate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs! Telegram | Youtube | LinkedIn | Instagram | Facebook | Twitter | Pinterest « Prev - Laplace Transform Questions and Answers – Convolution » Next - Ordinary Dierential Equations Questions and Answers – Table of General Properties

https://www.sanfoundry.com/ordinary-differential-equations-multiple-choice-questions-answers/



5/7

3/31/2021

Ordinary Differential Equations Multiple Choice Questions and Answers - Sanfoundry

1. Home 2. Digital Signal Processing Questions and Answers 3. Mathematics Questions and Answers – Class 12 4. Digital Image Processing Questions and Answers 5. MATLAB Questions and Answers 6. Electric Circuits Questions and Answers 7. Network Theory Questions and Answers 8. Numerical Methods Questions and Answers 9. Signals & Systems Questions and Answers 10. Engineering Mathematics Questions and Answers 11. Ordinary Dierential Equations Questions and Answers – Special Functions – 2 (Beta) 12. Ordinary Dierential Equations Questions and Answers – Orthogonal Trajectories 13. Engineering Mathematics Questions and Answers – Laplace Transform by Properties – 1 14. Engineering Mathematics Questions and Answers – Existence and Laplace Transform of Elementary Functions – 2 15. Signals & Systems Questions and Answers – The Laplace Transform 16. Ordinary Dierential Equations Questions and Answers – Basic Denitions 17. Ordinary Dierential Equations Questions and Answers – Clairaut’s and Lagrange Equations 18. Ordinary Dierential Equations Questions and Answers – Special Functions – 4 (Legendre) 19. Ordinary Dierential Equations Questions and Answers – Reducible to Homogenous Form 20. Ordinary Dierential Equations Questions and Answers – Method of Undetermined Coecients advertisement



https://www.sanfoundry.com/ordinary-differential-equations-multiple-choice-questions-answers/

6/7

3/31/2021

Ordinary Differential Equations Multiple Choice Questions and Answers - Sanfoundry

professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn

Subscribe Sanfoundry Newsletter and Posts Name*

Email*

Subscribe

About | Certications | Internships | Jobs | Privacy Policy | Terms | Copyright | Contact













© 2011-2021 Sanfoundry. All Rights Reserved.



https://www.sanfoundry.com/ordinary-differential-equations-multiple-choice-questions-answers/

7/7...