What is the order of the differential equation, y”+y’-x3y=sinx?

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

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

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

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

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 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 differential equation $$\frac{{{\text{dy}}}}{{{\text{dx}}}} + 4{\text{y}} = 5$$ is valid in the domain 0 ≤ x ≤ 1 with y(0) = 2.25. The solution of differential equation is

A

y = e^-4x + 1.25

B

y = e^-4x + 5

C

y = e^4x + 5

D

y = e^4x + 1.25

Consider the differential equation $${{\text{x}}^2}\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + {\text{x}}\frac{{{\text{dy}}}}{{{\text{dx}}}} - {\text{y}} = 0.$$ Which of the following is a solution to this differential equation for x > 0 ?

A

e^x

B

x²

C

$$\frac{1}{{\text{x}}}$$

D

$$l$$n x

Which of the following instances can be held to be final orders?
1. An order of a High Court dismissing an appeal for the appellant's failure to furnish order
2. An order that an appeal had abated
3. An order in a revision reversing the dismissal of a suit and restoring it to the file of the lower court when such an order had the effect of reinstating a primary decree
4. An order refusing an application under section 45 of the Specific Relief Act 1 of 1877
5. An order passed by a High Court in insolvency proceedings

A

2, 3

B

1, 4

C

1, 5, 6

D

All of these

What is the order of the differential equation, y”+y’-x3y=sinx?

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