Ordinary Differential Equations Questions and Answers – Basic Definitions

«
»

This set of Ordinary Differential Equations Multiple Choice Questions & Answers (MCQs) focuses on “”.

1. Which of the following correctly defines ordinary differential equations?
a) A differential equation in which a dependent variable (say ‘y’) depends on only one independent variable (say ’x’)
b) A differential equation in which an independent variable (say ‘y’) depends on only one dependent variable (say ’x’)
c) A differential equation in which a dependent variable (say ‘y’) depends on one or more independent variables (say ’x’, ’t’ etc.)
d) A differential equation in which an independent variable (say ‘y’) depends on one or more dependent variables (say ’x’, ’t’ etc.)
View Answer

Answer: a
Explanation: A differential equation is an equation involving an unknown function y of one or more independent variables x, t, …… and its derivatives. These are divided into two types, ordinary or partial differential equations.
An ordinary differential equation is a differential equation in which a dependent variable (say ‘y’) is a function of only one independent variable (say ‘x’).
advertisement

2. A partial differential equation is one in which a dependent variable (say ‘y’) depends on one or more independent variables (say ’x’, ’t’ etc.)
a) False
b) True
View Answer

Answer: b
Explanation: An ordinary differential equation is divided into two types, ordinary and partial differential equations.
A partial differential equation is one in which a dependent variable depends on one or more independent variables.
Example: \(F(x,t,y,\frac{∂y}{∂x},\frac{∂y}{∂t},……)= 0 \)

3. What is the order of the differential equation, y”+y’-x3y=sinx?
a) 2
b) 1
c) 0
d) 3
View Answer

Answer: a
Explanation: Order of a differential equation is given by the highest order derivative appearing in the differential equation. Hence for the given equation, y”+y’-x3y=sinx, the order is 2.

4. What is the degree of the differential equation, 4x3-6x2 y3+2y=0?
a) 3
b) 5
c) 1
d) 8
View Answer

Answer: b
Explanation: The degree of an equation that has not more than one variable in each term is the exponent of the highest power to which that variable is raised in the equation. But when more than one variable appears in a term, it is necessary to add the exponents of the variables within a term to get the degree of the equation. Hence, the degree of the equation, 4x3-6x2 y3+2y=0, is 2+3 = 5.

5. Which one of the following is not a criterion for linearity of an ordinary differential equation?
a) The dependent variable y and its derivatives are of first degree
b) The derivatives of the dependent variable y should be of second degree
c) No product terms of y and/or any of its derivatives are present
d) No transcendental functions of y and/or its derivatives occur
View Answer

Answer: b
Explanation: The criterions for linearity of an ordinary differential equation are:

  • The dependent variable y and its derivatives are of first degree
  • No product terms of y and/or any of its derivatives are present
  • No transcendental functions of y and/or its derivatives occur
advertisement

6. Which of the following is a type of Iterative method of solving non-linear equations?
a) Graphical method
b) Interpolation method
c) Trial and Error methods
d) Direct Analytical methods
View Answer

Answer: b
Explanation: There are 2 types of Iterative methods, (i) Interpolation methods (or Bracketing methods) and (ii) Extrapolation methods (or Open-end methods).

7. Which of the following is not an example of linear differential equation?
a) y=mx+c
b) x+x’=0
c) x+x2=0
d) x”+2x=0
View Answer

Answer: c
Explanation: For a differential equation to be linear the dependent variable should be of first degree. Since in equation x+x2=0, x2 is not a first power, it is not an example of linear differential equation.

8. Which of the following is not a standard method for finding the solutions for differential equations?
a) Variable Separable
b) Homogenous Equation
c) Bernoulli’s Equation
d) Orthogonal Method
View Answer

Answer: d
Explanation: The following are the different standard methods used in finding the solution of a differential equation:

  • Variable Separable
  • Homogenous Equation
  • Non-homogenous Equation reducible to Homogenous Equation
  • Exact Differential Equation
  • Non-exact Differential Equation that can be made exact with the help of integrating factors
  • Linear First Order Equation
  • Bernoulli’s Equation

9. Solution of a differential equation is any function which satisfies the equation.
a) False
b) True
View Answer

Answer: b
Explanation: A solution of a differential equation is any function which satisfies the equation, i.e., reduces it to an identity. A solution is also known as integral or primitive.
advertisement

10. The equation \(2\frac{dy}{dx} – xy = y^{-2},\) is an example for Bernoulli’s equation.
a) False
b) True
View Answer

Answer: b
Explanation: A first order, first degree differential equation of the form,
\(\frac{dy}{dx} + P(x). y = Q(x). y^a,\) is known as Bernoulli’s equation.

Sanfoundry Global Education & Learning Series – Ordinary Differential Equations.

To practice all areas of Ordinary Differential Equations, here is complete set of 1000+ Multiple Choice Questions and Answers.

Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

advertisement
advertisement
advertisement

Leave a Comment

Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT 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