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INTEGRATING FACTOR – MCQ – LEVEL – 1

INTEGRATING FACTOR – MCQ – LEVEL – 1

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Question 1 of 10

1. Question
The integrating factor for the differential equation $\left ( x + 1 \right ) \dfrac{dy}{dx} - y = e^{3x} (x + 1)^2$ is :
- $\dfrac{1}{x + 1}$
- $x + 1$
- $\dfrac{1}{x^2 + 1}$
- $x^2 + 1$
Correct

Incorrect
Question 2 of 10

2. Question
Integrating factor for the differential equation $\dfrac{1}{x}{y}' - \dfrac{1}{x^2} y = x$ would be :
- $x$
- $x^2$
- $x^{-1}$
- $x^{-2}$
Correct

Incorrect
Question 3 of 10

3. Question
Which of the following differential equations can be made exact by multiplying by $x^2 ~?$

$P : \dfrac{dy}{dx} + \dfrac{2}{x}y = 4$

$Q : x\dfrac{dy}{dx} + 3y = x^2$

$R : \dfrac{1}{x} \dfrac{dy}{dx} - \dfrac{1}{x^2} y = x$

$S = \dfrac{1}{x} \dfrac{dy}{dx} + \dfrac{1}{x^2}y = 3$
- $P ~\mathrm{and}~ Q$
- $R ~\mathrm{and}~ S$
- $P, Q ~\mathrm{and}~ R$
- $P, Q ~\mathrm{and}~ S$
Correct

Incorrect
Question 4 of 10

4. Question
The integrating factor of the differential equation $2ydx + xdy = 0$ is :
- $x$
- $y$
- $x y$
- $y^2$
Correct

Incorrect
Question 5 of 10

5. Question
The differential equation $(axy^2 + by)dx + (bx^2 y + ax)dy = 0$ is exact iff :
- $a \geq b$
- $a \leq b$
- $a \neq b$
- $a = b$
Correct

Incorrect
Question 6 of 10

6. Question
If integrating factor for the differential equation ${y}' + y \cot c = \mathrm{cosec}~ x$ would be :
- $\sin x$
- $\cos x$
- $\sec x$
- $\tan x$
Correct

Incorrect
Question 7 of 10

7. Question
Integrating factor of the linear differential equation ${y}' + \dfrac{3y}{x + 1} = (x + 1)^4,$ will be :
- $x + 1$
- $(x + 1)^3$
- $\dfrac{1}{x+1}$
- $\dfrac{1}{(x + 1)^3}$
Correct

Incorrect
Question 8 of 10

8. Question
The differential equation $dy - \left ( \dfrac{e^x}{x^3} - \dfrac{3y}{x} \right )dx = 0$ can be made
- $x$
- $x^2$
- $x^3$
- $x^4$
Correct

Incorrect
Question 9 of 10

9. Question
The integrating factor of the differential equation $e^x \cos y ~dx - e^x \sin y ~dy = 0$ is :
- $\sin x$
- $\cos y$
- $\sin x \cos y$
- Not applicable
Correct

Incorrect
Question 10 of 10

10. Question
The integrating factor of the differential equation $\dfrac{dy}{dx} = -\dfrac{(3xy +y^2)}{x^2 + xy}$ would be :
- $x^4$
- $x^3$
- $x^2$
- $x$
Correct

Incorrect

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