Homogeneous Equations are those in which the dependent variable (and its derivatives) appear in terms with degree exactly one.
a) True
b) False
Q.2.
Which of the following is false regarding quasilinear equations?
a) All the terms with highest order derivatives of dependent variables occur linearly
b) The coefficients of terms with highest order derivatives of dependent variables are functions of only lower order derivatives of the dependent variables
c) Lower order derivatives can occur in any manner
d) All the terms with lower order derivatives of dependent variables occur linearly
Q.3.
Which of the following is false regarding Bessel polynomials?
a) Krall and Fink (1949) defined the Bessel polynomials
b) The polynomials satisfy the recurrence formula
c) The solutions of homogeneous equations are closely related to Bessel polynomials
d) Bessel polynomials are not an orthogonal sequence of polynomials
Q.4.
The solution of an ODE contains arbitrary constants, the solution to a PDE contains arbitrary functions.
a) True
b) False
Q.5.
A homogeneous linear differential equation has constant coefficients if it has the form
a) False
b) True
Q.6.
The symbol used for partial derivatives, ∂, was first used in mathematics by Marquis de Condorcet.
a) True
b) False
Q.7.
Which of the following is true with respect to formation of differential equation by elimination of arbitrary constants?
a) The given equation should be differentiated with respect to independent variable
b) Elimination of the arbitrary constant by replacing it using derivative
c) If ‘n’ arbitrary constant is present, the given equation should be differentiated ‘n’ number of times
d) To eliminate the arbitrary constants, the given equation must be integrated with respect to the dependent variable
Q.8.
In the formation of differential equation by elimination of arbitrary constants, after differentiating the equation with respect to independent variable, the arbitrary constant gets eliminated.
a) False
b) True
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