Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

151.

A homogeneous differential equation of the form dx/dy = f(x/y) can be solved by making substitution,(a) x = vy (b) y = vx (c) y = v (d) x = v

Answer»

The correct answer is : (a) x = vy 
Discussion
152.

A homogeneous differential equation of the form dy/dx = f(y/x) can be solved by making substitution (a) y = vx(b) v = yx (c) x = vy (d) x = v

Answer»

The correct answer is : (a) y = vx
Discussion
153.

If the surrounding air is kept at 20°C and the body cools from 80°C to 70°C in 5 minutes, the temperature of the body after 15 minutes will be….. (a) 51.7°C (b) 54.7°C (c) 52.7°C (d) 50.7°C

Answer»

Correct option is: (b) 54.7°C
Discussion
154.

Find the order and degree of the following differential equations.(i) dy/dx + 2 y = x3(ii) d3y/dx3  + 3(dy/dx)3 + 2(dy/dx) = 0(iii) d2y/dx2 = √(y - dy/dx)(iv) d3y/dx3 = 0

Answer»

(i) dy/dx + 2 y = x3

Highest order derivative is dy/dx

power of dy/dx is 1

∴ order = 1    Degree = 1

(ii) d3y/dx3  + 3(dy/dx)3 + 2(dy/dx) = 0

Highest order derivative is d3y/dx3

Power of d3y/dx3  = 1

∴ order = 3    Degree = 1

(iii) d2y/dx2 = √(y - dy/dx)

Here we eliminate the radical sign. squaring both sides we get,

(d2y/dx2)2  = (y - dy/dx)

∴ order = 2    Degree = 2

(iv) d3y/dx3 = 0

order = 3,     Degree = 1
Discussion
155.

Find the order and degree of the following differential equations.i. d2y/dx2 + y + (dy/dx - d3y/dx3)3/2 = 0ii. (2 - y")2 = y"2 + 2y'iii. (dy/dx)3 + y = x - dx/dy

Answer»

i. d2y/dx2 + y + (dy/dx - d3y/dx3)3/2 = 0

Here we elimenate the radical sign

For this write the equation as  d2y/dx2 + y = -(dy/dx - d3y/dx3)3/2

Squaring both the sides, we get (d2y/dx2 + y)2 = (dy/dx - d3y/dx3)3

∴ Order = 3, Degree = 3

ii. (2 - y")2 = y"2 + 2y'

4 - 4y" + (y")2 = (y")2 + 2y'

⇒ 4 - 4y" = 2y'

∴ Order = 2, Degree = 1

iii. (dy/dx)3 + y = x - dx/dy

multiplting the equation by dy/dx

(dy/dx)4 + y(dy/dx) = x(dy/dx) - 1

∴ Order = 1,     Degree = 4
Discussion
156.

The differential equation is (dx/dy)3 + 2y1/2 = x is _________ (a) of order 2 and degree 1 (b) of order 1 and degree 3 (c) of order 1 and degree 6 (d) of order 1 and degree 2

Answer»

(b) of order 1 and degree 3
Discussion