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Test: First Order Nonlinear PDE - Civil Engineering (CE) MCQ


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10 Questions MCQ Test Engineering Mathematics - Test: First Order Nonlinear PDE

Test: First Order Nonlinear PDE for Civil Engineering (CE) 2024 is part of Engineering Mathematics preparation. The Test: First Order Nonlinear PDE questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: First Order Nonlinear PDE MCQs are made for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: First Order Nonlinear PDE below.
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Test: First Order Nonlinear PDE - Question 1

Which of the following represents Lagrange’s linear equation?

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

Test: First Order Nonlinear PDE - Question 2

Which of the following equations represents Clairaut’s partial differential equation?

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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).

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Test: First Order Nonlinear PDE - Question 3

Which of the following is a type of Iterative method of solving non-linear equations?

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

Test: First Order Nonlinear PDE - Question 4

Which of the following is not a standard method for finding the solutions for differential equations?

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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
Test: First Order Nonlinear PDE - Question 5

Which of the following is an example of non-linear differential equation?

Detailed Solution for Test: First Order Nonlinear PDE - Question 5

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.

Test: First Order Nonlinear PDE - Question 6

Solution of a differential equation is any function which satisfies the equation.

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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.

Test: First Order Nonlinear PDE - Question 7

A solution which does not contain any arbitrary constants is called a general solution.

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

Test: First Order Nonlinear PDE - Question 8

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.

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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.

Test: First Order Nonlinear PDE - Question 9

A particular solution for an equation is derived by substituting particular values to the arbitrary constants in the complete solution.

Detailed Solution for Test: First Order Nonlinear PDE - Question 9

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.

Test: First Order Nonlinear PDE - Question 10

For the equation ay/dx 7x2y = 0, if y(0) = 3/7, then the value of y(1) is

Detailed Solution for Test: First Order Nonlinear PDE - Question 10

Concept:

For solving first order, first-degree differential equations always first inspect with variable separation method.

Calculation:

Given the differential equation is,

Where A is a constant.

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