The Integrating factor of a differential equation is also called the primitive.

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

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

The integrating factor for differential equation $$\frac{{{\text{dP}}}}{{{\text{dt}}}} + {{\text{k}}_2}{\text{P}} = {{\text{k}}_1}{{\text{L}}_0}{{\text{e}}^{ - {{\text{k}}_1}{\text{t}}}}$$ is

A

e^-k₁t

B

e^-k₂t

C

e^k₁t

D

e^k₂t

Consider the following types of digital voltmeters: 1. Ramp type 2. Dual slope integrating type 3. Integrating type using voltage to frequency conversion 4. Successive approximation type 5. Servo balanced potentiometer type Which of these require a fixed reference voltage at the comparator stage?

A

1 and 2 only

B

3, 4 and 5 only

C

2 and 3 only

D

1, 4 and 5 only

A class III mathematics teacher gave the following questions to her students: $\begin{equation} \frac{ \begin{array}[b]{r} 256 \\ + 173 \end{array} }{ } \end{equation}$ $\begin{equation} \frac{ \begin{array}[b]{r} 28 \\ + 32 \end{array} }{ } \end{equation}$ $\begin{equation} \frac{ \begin{array}[b]{r} 129 \\ + 76 \end{array} }{ } \end{equation}$ Later she asks the students to solve a worksheet that has similar questions. Which of the following statements is appropriate for the given situation?

A

It is an example of contextual question

B

It is an example of open ended task

C

Teacher should have asked the students to solve ten more such questions as a home task to save the time

D

The tasks is based on drill and practice and should be discouraged at primary level

A table for which, a primitive defines groups of attribute values to be used when displaying that primitive on a particular output device is called

A

Bundle table

B

Index table

C

Both a and b

D

None of these

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

Consider the following second-order differential equation: y" - 4y' + 3y = 2t - 3t²
The particular solution of the differential equation is

A

-2 - 2t - t²

B

-2t - t²

C

2t - t²

D

-2 - 2t - 3t²

Consider the differential equation $$\left( {{{\text{t}}^2} - 81} \right)\frac{{{\text{dy}}}}{{{\text{dt}}}} + 5{\text{ty}} = \sin \left( {\text{t}} \right)$$ with y(1) = 2π. Thereexists a unique solution for this differential equation when t belongs to the interval

A

(-2, 2)

B

(-10, 10)

C

(-10, 2)

D

(0, 10)

A differential equation is given as
$${{\text{x}}^2}\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} - 2{\text{x}}\frac{{{\text{dy}}}}{{{\text{dx}}}} + 2{\text{y}} = 4$$
The solution of differential equation in terms of arbitrary constant C₁ and C₂ is

A

$${\text{y}} = \frac{{{{\text{C}}_1}}}{{{{\text{x}}^2}}} + {{\text{C}}_2}{\text{x}} + 2$$

B

$${\text{y}} = {{\text{C}}_1}{{\text{x}}^2} + {{\text{C}}_2}{\text{x}} + 4$$

C

$${\text{y}} = {{\text{C}}_1}{{\text{x}}^2} + {{\text{C}}_2}{\text{x}} + 2$$

D

$${\text{y}} = \frac{{{{\text{C}}_1}}}{{{{\text{x}}^2}}} + {{\text{C}}_2}{\text{x}} + 2$$

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

The Integrating factor of a differential equation is also called the primitive.

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