Which one of the following is not a criterion for linearity of an ordinary differential equation?

What is the price range of ordinary wall clocks ? I. The price range of ordinary wrist watches of company X is Rs 400 to Rs 600. II. The price range of ordinary wall clocks of company X is 50 percent that of their ordinary watches.

A

If the data in statement I alone are sufficient to answer the question

B

If the data in statement II alone are sufficient answer the question

C

If the data either in I or II alone are sufficient to answer the question;

D

If the data even in both the statements together are sufficient to answer the question

The figure shows the plot of y as a function of x
Differential Equations mcq question image

The function shown is the solution of the differential equation (assuming all initial conditions to be zero) is

A

$$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} = 1$$

B

$$\frac{{{\text{dy}}}}{{{\text{dx}}}} = {\text{x}}$$

C

$$\frac{{{\text{dy}}}}{{{\text{dx}}}} = - {\text{x}}$$

D

$$\frac{{{\text{dy}}}}{{{\text{dx}}}} = \left| {\text{x}} \right|$$

Which one of the following is not a criterion for linearity of an equation?

A

The dependent variable y should be of second order

B

The derivatives of the dependent variable should be of second order

C

Each coefficient does not depend on the independent variable

D

Each coefficient depends only on the independent variable

In specification analysis, assumptions related to linearity states but linearity must be within

A

irrelevant range

B

relevant range

C

significant range

D

insignificant range

While solving an Ordinary Differential 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 if the initial conditions are zero.

A

True

B

False

An ordinary differential equation is given below.
$$\left( {\frac{{{\text{dy}}}}{{{\text{dx}}}}} \right)\left( {{\text{x}}\ln {\text{x}}} \right) = {\text{y}}$$
The solution for the above equation is
(Note: K denotes a constant in the options)

A

y = Kxe^x

B

y = Kxe^-x

C

y = Klnx

D

y = Kxlnx

Biotransformation of an organic compound having concentration (x) can be modeled using an ordinary differential equation $$\frac{{{\text{dx}}}}{{{\text{dt}}}} + {\text{k}}{{\text{x}}^2} = 0,$$ where k is the reaction rate constant. If x = a at t = 0, the solution of the equation is

A

x = ae^-kt

B

$$\frac{1}{{\text{x}}} = \frac{1}{{\text{a}}} + {\text{kt}}$$

C

x = a(1 - e^-kt)

D

x = a + kt

Consider the differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} = 1 + {{\text{y}}^2}.$$
Which one of the following can be a particular solution of this differential equation?

A

y = tan(x + 3)

B

y = tan x + 3

C

x = tan(y + 3)

D

x = tan y + 3

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

Linear partial differential equations are reduced to ordinary differential equations in which of these methods?

A

Change of variables

B

Fundamental equations

C

Superposition principle

D

Separation of variables

Which one of the following is not a criterion for linearity of an ordinary differential equation?

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