Class 12 Mathematics - Chapter 9: Differential Equations MCQ Questions

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Question 1

The differential equation which represents the family of curves y = e^c₂x, where c₁ and c₂ are arbitrary constants, is:

A y’ = yÂ²

B yy” = (y’)Â²

C yy” = y’

D y” = y’y

Question 2

((frac { dy }{dx}))Â² – x (frac { dy }{dx}) + y = 0 is

A y = 2xÂ² – 4.

B y = 2x – 4

C y = 2x

D y = 2

Question 3

(1 – yÂ²) (frac { dy }{dx}) + yx = ay(-1 < y < 1) is

A (frac { 1 }{sqrt{1-y^2}})

B (frac { 1 }{1-y^2})

C (frac { 1 }{sqrt{y^2-1}})

D (frac { 1 }{y^2-1})

Question 4

The integrating factor of the differential equation x(frac { dy }{dx}) – y = 2xÂ² is

A x

B (frac { 1 }{x})

C e^-y

D e^-x

Question 5

Which of the following differential equations has y = c₁ e^x+ c₂ e^-x as the general solution?

A (frac { d^2y }{dx^2}) – 1 = 0

B (frac { d^2y }{dx^2}) + 1 = 0

C (frac { d^2y }{dx^2}) – y = 0

D (frac { d^2y }{dx^2}) + y = 0

Question 6

The number of arbitrary constants in the general solution of a differential equation of fourth order is:

A 4.

B 3

C 2

Question 7

((frac { d^2y }{dx^2}))Â³ + ((frac { dy }{dx}))Â² + sin ((frac { dy }{dx})) + 1 = 0 is

A not defined.

B 1

C 2

D 3

Question 8

(frac { d^2y }{dx^2}) + 3((frac { dy }{dx}))Â² = xÂ² log ((frac { d^2y }{dx^2})) is

A not defined

B 3

C 2

D 1

Question 9

x(frac { dy }{dx}) + 2y = xÂ² is

A y = y = (frac { x^4+c }{4x^2})

B y = y = (frac { x^4+c }{x^2})

C y = (frac { x^2 }{4}) + c

D y = (frac { x^2+c }{4x^2})

Question 10

If the firm employs 25 more workers, then the new level of production of items is:

A 2500.

B 4500

C 3500

D 3000

Question 11

The degree of the differential equation representing the family of curves (x – a)Â² + yÂ² = 16 is

A 1.

B 3

C 2

Question 12

The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is

A (y – 2)Â² y’Â² = 25 – (y – 2)Â².

B (y – 2) y’Â² =25 – (y – 2)Â².

C (x – 2) y’Â² = 25 – (y – 2)Â²

D (x – 2)Â² y’Â² = 25 – (y – 2)Â²

Question 13

Which of the following differential equations has y = x as one of its particular solutions?

A (frac { d^2y }{dx^2}) + x (frac { dy }{dx}) + xy = 0

B (frac { d^2y }{dx^2}) – xÂ² (frac { dy }{dx}) + xy = 0

C (frac { d^2y }{dx^2}) + x (frac { dy }{dx}) + xy = x

D (frac { d^2y }{dx^2}) – xÂ² (frac { dy }{dx}) + xy = x

Question 14

The number of arbitrary constants in the particular solution of a differential equation of third order is:

A 0.

B 1

C 2

D 3

Question 15

cos x dy = y (sin x – y) dx, 0 < x < (frac { Ï€ }{2}) is

A tan x = (sec x + c)y.

B y tan x = sec x + c

C y sec x = tan x + c

D sec x = (tan x + c)y

Question 16

The general solution of the differential equation (frac { dy }{dx}) = e^x+y is

A e^-x + e^-y = c.

B e^-x + e^y = c

C e^x + e^y = c

D e^x + e^-y = c

Question 17

Which of the following differential equations cannot be solved, using variable separable method?

A (frac { dy }{dx}) + y = 2.

B xy (frac { dy }{dx}) = 1 + x + y + xy

C (yÂ² – 2xy) dx = (xÂ² – 2xy) dy

D (frac { dy }{dx}) + e^x+y + e^-x+y

Question 18

[1 + ((frac { dy }{dx}))Â²]Â² = (frac { d^2y }{dx^2})

A 4, 2.

B 2, 1

C 2, 2

D 1, 2

Question 19

2x (frac { dy }{dx}) – y = 3 represents a family of:

A ellipses.

B parabolas

C circles

D straight lines

Question 20

Which of the following is a homogeneous differential equation?

A yÂ² dx + (xÂ² – xy – yÂ²)dy = 0.

B (xÂ³ + 2yÂ²) dx + 2xy dy = 0

C xy dx – (xÂ³ + yÂ²)dy = Q

D (4x + 6y + 5)dy – (3y + 2x + 4)dx = 0

Question 21

e^x dy + (y e^x + 2x) dx = 0 is

A y e^x + xÂ² = c.

B y e^x + xÂ² = c

C x e^y + yÂ² = c

D x e^x + xÂ² = c

Question 22

A homogeneous differential equation of the form (frac { dy }{dx}) = h((frac { x }{y})) can be solved by making the substitution.

A x = v

B x = vy

C v = yx

D y = vx

Question 23

The general solution of the differential equation (frac { y dx – x dy }{y}) = 0 is

A y = cxÂ².

B y = cx

C x = cyÂ²

D xy = c

Question 24

2xÂ² (frac { d^2y }{dx^2}) – 3 (frac { dy }{dx}) + y = 0 is

A not defined.

C 1

D 2

Question 25

The general solution of a differential equation of the type (frac { dy }{dx}) + P₁ x = Q₁ is:

A x e^{âˆ«p₁ dx} = âˆ«(Q₁ e^{âˆ«p₁ dx}) dx + c

B x e^{âˆ«p₁ dy} = âˆ«(Q₁ e^{âˆ«p₁ dy}) dy + c

C y e^{âˆ«p₁ dx} = âˆ«(Q₁ e^{âˆ«p₁ dx}) dx + c

D y e^{âˆ«p₁ dy} = âˆ«(Q₁ e^{âˆ«p₁ dy}) dy + c

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Class 12 Mathematics - Chapter 9: Differential Equations MCQ Questions

Your Class 12 Mathematics Study Path

The differential equation which represents the family of curves y = e^c₂x, where c₁ and c₂ are arbitrary constants, is:

((frac { dy }{dx}))Â² – x (frac { dy }{dx}) + y = 0 is

(1 – yÂ²) (frac { dy }{dx}) + yx = ay(-1 < y < 1) is

The integrating factor of the differential equation x(frac { dy }{dx}) – y = 2xÂ² is

Which of the following differential equations has y = c₁ e^x+ c₂ e^-x as the general solution?

The number of arbitrary constants in the general solution of a differential equation of fourth order is:

((frac { d^2y }{dx^2}))Â³ + ((frac { dy }{dx}))Â² + sin ((frac { dy }{dx})) + 1 = 0 is

(frac { d^2y }{dx^2}) + 3((frac { dy }{dx}))Â² = xÂ² log ((frac { d^2y }{dx^2})) is

x(frac { dy }{dx}) + 2y = xÂ² is

If the firm employs 25 more workers, then the new level of production of items is:

The degree of the differential equation representing the family of curves (x – a)Â² + yÂ² = 16 is

The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is

Which of the following differential equations has y = x as one of its particular solutions?

The number of arbitrary constants in the particular solution of a differential equation of third order is:

cos x dy = y (sin x – y) dx, 0 < x < (frac { Ï€ }{2}) is

The general solution of the differential equation (frac { dy }{dx}) = e^x+y is

Which of the following differential equations cannot be solved, using variable separable method?

[1 + ((frac { dy }{dx}))Â²]Â² = (frac { d^2y }{dx^2})

2x (frac { dy }{dx}) – y = 3 represents a family of:

Which of the following is a homogeneous differential equation?

e^x dy + (y e^x + 2x) dx = 0 is

A homogeneous differential equation of the form (frac { dy }{dx}) = h((frac { x }{y})) can be solved by making the substitution.

The general solution of the differential equation (frac { y dx – x dy }{y}) = 0 is

2xÂ² (frac { d^2y }{dx^2}) – 3 (frac { dy }{dx}) + y = 0 is

The general solution of a differential equation of the type (frac { dy }{dx}) + P₁ x = Q₁ is:

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Class 12 Mathematics - Chapter 9: Differential Equations MCQ Questions

Your Class 12 Mathematics Study Path

The differential equation which represents the family of curves y = ec2x, where c1 and c2 are arbitrary constants, is:

((frac { dy }{dx}))Â² – x (frac { dy }{dx}) + y = 0 is

(1 – yÂ²) (frac { dy }{dx}) + yx = ay(-1 < y < 1) is

The integrating factor of the differential equation x(frac { dy }{dx}) – y = 2xÂ² is

Which of the following differential equations has y = c1 ex+ c2 e-x as the general solution?

The number of arbitrary constants in the general solution of a differential equation of fourth order is:

((frac { d^2y }{dx^2}))Â³ + ((frac { dy }{dx}))Â² + sin ((frac { dy }{dx})) + 1 = 0 is

(frac { d^2y }{dx^2}) + 3((frac { dy }{dx}))Â² = xÂ² log ((frac { d^2y }{dx^2})) is

x(frac { dy }{dx}) + 2y = xÂ² is

If the firm employs 25 more workers, then the new level of production of items is:

The degree of the differential equation representing the family of curves (x – a)Â² + yÂ² = 16 is

The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is

Which of the following differential equations has y = x as one of its particular solutions?

The number of arbitrary constants in the particular solution of a differential equation of third order is:

cos x dy = y (sin x – y) dx, 0 < x < (frac { Ï€ }{2}) is

The general solution of the differential equation (frac { dy }{dx}) = ex+y is

Which of the following differential equations cannot be solved, using variable separable method?

[1 + ((frac { dy }{dx}))Â²]Â² = (frac { d^2y }{dx^2})

2x (frac { dy }{dx}) – y = 3 represents a family of:

Which of the following is a homogeneous differential equation?

ex dy + (y ex + 2x) dx = 0 is

A homogeneous differential equation of the form (frac { dy }{dx}) = h((frac { x }{y})) can be solved by making the substitution.

The general solution of the differential equation (frac { y dx – x dy }{y}) = 0 is

2xÂ² (frac { d^2y }{dx^2}) – 3 (frac { dy }{dx}) + y = 0 is

The general solution of a differential equation of the type (frac { dy }{dx}) + P1 x = Q1 is:

Practice Complete!

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The differential equation which represents the family of curves y = e^c₂x, where c₁ and c₂ are arbitrary constants, is:

Which of the following differential equations has y = c₁ e^x+ c₂ e^-x as the general solution?

The general solution of the differential equation (frac { dy }{dx}) = e^x+y is

e^x dy + (y e^x + 2x) dx = 0 is

The general solution of a differential equation of the type (frac { dy }{dx}) + P₁ x = Q₁ is: