Partial Differential Equations Questions and Answers – First Order Non-Linear PDE

«
»

This set of Fourier Analysis and Partial Differential Equations Multiple Choice Questions & Answers (MCQs) focuses on “First Order Non-Linear PDE”.

1. Which of the following is an example of non-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.
advertisement

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

Answer: c
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

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

Answer: a
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.

4. A solution which does not contain any arbitrary constants is called a general solution.
a) True
b) False
View Answer

Answer: a
Explanation: The solution of a partial differential equation obtained by eliminating the arbitrary constants is called a general solution.

5. 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).
advertisement

6. A particular solution for an equation is derived by substituting particular values to the arbitrary constants in the complete solution.
a) True
b) False
View Answer

Answer: a
Explanation: A solution which does not contain any arbitrary constants is called a general solution whereas a particular solution is derived by substituting particular values to the arbitrary constants in this solution.

7. Singular solution of a differential equation is one that cannot be obtained from the general solution gotten by the usual method of solving the differential equation.
a) True
b) False
View Answer

Answer: a
Explanation: A differential equation is said to have a singular solution if in all points in the domain of the equation the uniqueness of the solution is violated. Hence, this solution cannot be obtained from the general solution.

8. Which of the following equations represents Clairaut’s partial differential equation?
a) z=px+f(p,q)
b) z=f(p,q)
c) z=p+q+f(p,q)
d) z=px+qy+f(p,q)
View Answer

Answer: d
Explanation: Equations of the form, z=px+qy+f(p,q) are known as Clairaut’s partial differential equations, named after the Swiss mathematician, A. C. Clairaut (1713-1765).

9. Which of the following represents Lagrange’s linear equation?
a) P+Q=R
b) Pp+Qq=R
c) p+q=R
d) Pp+Qq=P+Q
View Answer

Answer: b
Explanation: Equations of the form, Pp+Qq=R are known as Lagrange’s linear equations, named after Franco-Italian mathematician, Joseph-Louis Lagrange (1736-1813).
advertisement

10. A partial differential equation is one in which a dependent variable (say ‘x’) depends on an independent variable (say ’y’).
a) False
b) True
View Answer

Answer: a
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: \(F(x,t,y,\frac{∂y}{∂x},\frac{∂y}{∂t},……)= 0. \)

11. What is the complete solution of the equation, \(q= e^\frac{-p}{α}\)?
a) \(z=ae^\frac{-a}{α}y\)
b) \(z=x+e^\frac{-a}{α}y\)
c) \(z=ax+e^\frac{-a}{α} y+c\)
d) \(z=e^\frac{-a}{α}y\)
View Answer

Answer: c
Explanation: Given: \(q= e^\frac{-p}{α}\)
The given equation does not contain x, y and z explicitly.
Setting p = a and q = b in the equation, we get \(b= e^\frac{-a}{α}.\)
Hence, a complete solution of the given equation is,
\(z=ax+by+c,\,with \, b= e^\frac{-a}{α}\)
\(z=ax+e^\frac{-a}{α} y+c.\)

12. A particular solution for an equation is derived by eliminating arbitrary constants.
a) True
b) False
View Answer

Answer: b
Explanation: A particular solution for an equation is derived by substituting particular values to the arbitrary constants in the complete solution thereby eliminating any arbitrary constants present in the solution. Such solution represents a particular member of the family of surfaces given by the complete solution.

Sanfoundry Global Education & Learning Series – Fourier Analysis and Partial Differential Equations.

advertisement

To practice all areas of Fourier Analysis and Partial 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