Calculus

Differential Equations

Easy

common

Match the LIST-I with LIST-II

LIST-I Differential equation LIST-II Order and degree
A. $y'' = [1+(y')^2]^{3/2}$ I. 3, 4
B. $y''' + y' + y = 2x$ II. 2, 2
C. $2(y'')^3 - (y')^4 + y = 0$ III. 3, 1
D. $(y''')^4 + (y'')^3 + y' + y = 0$ IV. 2, 3

Choose the correct answer from the options given below:

LIST-I Differential equation	LIST-II Order and degree
A. $y'' = [1+(y')^2]^{3/2}$	I. 3, 4
B. $y''' + y' + y = 2x$	II. 2, 2
C. $2(y'')^3 - (y')^4 + y = 0$	III. 3, 1
D. $(y''')^4 + (y'')^3 + y' + y = 0$	IV. 2, 3

A - II, B - III, C - IV, D - I

A - III, B - II, C - IV, D - I

A - I, B - IV, C - II, D - III

A - IV, B - I, C - III, D - II

✅ Correct Option: 1

Order is the highest derivative present; degree is its power after removing radicals.

A: squaring gives $(y'')^2 = [1+(y')^2]^3$ , so order 2, degree 2 (II).

B: order 3, degree 1 (III).

C: order 2, degree 3 (IV).

D: order 3, degree 4 (I).

2026: 31 May Shift 2

Match the LIST-I with LIST-II

[ $a$ is an arbitrary constant]

	LIST-I Differential Equation		LIST-II Family of curves
A.	$x\,dy - y\,dx = 0$	I.	$x^2 + y^2 = a^2$
B.	$2y\,dx - x\,dy = 0$	II.	$y = ax$
C.	$x\,dx + y\,dy = 0$	III.	$y^2 = 16x + a$
D.	$y\,dy - 8\,dx = 0$	IV.	$x^2 = ay$

Choose the correct answer from the options given below:

2025: 2 June Shift 1

Match List-I with List-II

List-I	List-II
(A) The degree of differential equation $\frac{d^3y}{dx^3} = e^{\frac{dx}{dy}}$	(I) 2
(B) The order of differential equation $\left(\frac{dy}{dx}\right)^2 + \frac{d^3y}{dx^3} = 0$	(II) 4
(C) The sum of order and degree of differential equation $\frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) + \left(\frac{dy}{dx}\right)^5 = x$	(III) not defined
(D) The number of arbitrary constants in the general solution of a differential equation of order 2	(IV) 3

Choose the correct answer from the options given below:

2026: 29 May Shift 2

For the differential equation $\frac{d}{dx}\left(\frac{d^3y}{dx^3}\right)+\left(\frac{dy}{dx}\right)^3+y+x=7$ , which of the following statements are True?

A. Order of differential equation is 4

B. Number of arbitrary constants in the particular solution of differential equation are 4

C. Number of arbitrary constants in the general solution of the differential equation are 4

D. Degree of differential equation is 3

Choose the correct answer from the options given below:

2022: 25 May Shift 1

Solution of $\frac{dy}{dx} = (1+x^2)(1+y^2)$ is:

2026: 30 May Shift 1

The general solution of the differential equation $\frac{dy}{dx}-\frac{y}{x}+\text{cosec}\left(\frac{y}{x}\right)=0$ is

(Consider $\log x=\log_e x$ )

2025: 26 May Shift 2

Curd is at 80° F, five minutes later it came down at 60°F. After another 5 minutes, its temperature became 50° F. Given that the rate of change of temperature is proportional to (T - S), where S is temperature of the surroundings and T is temperature of the curd at any time t. Then the temperature of the surroundings is :

Solution

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