Calculus

Differential Equations

Medium

common

Match the LIST-I with LIST-II

LIST-I (Differential Equation) LIST-II (Order and degree)
A. $\log\left(\dfrac{dy}{dx}\right) + \dfrac{d^2y}{dx^2} = 0$ I. Order : 3 and degree : not defined
B. $\dfrac{d^3y}{dx^3} + y^2 + e^{\frac{dy}{dx}} = 4$ II. Order : 2 and degree : 2
C. $\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right)^2 + \dfrac{dy}{dx} = \sqrt{x}$ III. Order : 2 and degree : not defined
D. $\left(1+\left(\dfrac{dy}{dx}\right)^2\right)^{3/2} = \dfrac{d^2y}{dx^2}$ IV. Order : 2 and degree : 1

Choose the correct answer from the options given below:

	LIST-I (Differential Equation)		LIST-II (Order and degree)
A.	$\log\left(\dfrac{dy}{dx}\right) + \dfrac{d^2y}{dx^2} = 0$	I.	Order : 3 and degree : not defined
B.	$\dfrac{d^3y}{dx^3} + y^2 + e^{\frac{dy}{dx}} = 4$	II.	Order : 2 and degree : 2
C.	$\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right)^2 + \dfrac{dy}{dx} = \sqrt{x}$	III.	Order : 2 and degree : not defined
D.	$\left(1+\left(\dfrac{dy}{dx}\right)^2\right)^{3/2} = \dfrac{d^2y}{dx^2}$	IV.	Order : 2 and degree : 1

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

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

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

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

✅ Correct Option: 1

A: highest derivative is order $2$ , but the logarithm of a derivative makes degree undefined (III).

B: order $3$ , and $e^{dy/dx}$ leaves degree undefined (I).

C: expanding gives $2y'y''+y'=\sqrt{x}$ , order $2$ , degree $1$ (IV).

D: squaring gives $(1+y'^2)^3=(y'')^2$ , order $2$ , degree $2$ (II).

2026: 18 May Shift 1

Match List-I with List-II

List-I Differential equation	List-II Order and degree
(A) $\frac{d^4y}{dx^4} + \sin\left(\frac{d^3y}{dx^3}\right) = 0$	(I) order = 2, degree = 1
(B) $\left(\frac{d^2y}{dx^2}\right)^2 + \frac{dy}{dx} = 0$	(II) order = 3, degree = 1
(C) $\frac{d^3y}{dx^3} + y^2 + \frac{dy}{dx} = 0$	(III) order = 2, degree = 2
(D) $3y\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^4 = 0$	(IV) order = 4, degree not defined

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2026: 18 May Shift 2

The solution of the differential equation $9+y^2\dfrac{dy}{dx}=x^2$ is :

[Where $C$ is an arbitrary constant]

2026: 30 May Shift 2

Match List-I with List-II

Choose the correct answer from the options given below:

2025: 16 May Shift 1

The general solution of the differential equation $\frac{dy}{dx} + y \tan x = \sec x$

2025: 29 May Shift 2

Match List-I with List-II:

List-I	List-II
Differential Equations	Degree/Order
(A) Degree of the differential equation $\frac{d^3y}{dx^3} + 2 \log x.y = 0$	(I) 3
(B) Order of the differential equation $\frac{d^4y}{dx^4} + \left(\frac{dy}{dx}\right)^4 + xy = 0$	(II) 2
(C) Degree of the differential equation $\left(\frac{d^4y}{dx^4}\right)^2 + \left(\frac{dy}{dx}\right)^3 + x^2y = 0$	(III) 1
(D) Order of the differential equation $\frac{d^3y}{dx^3} + y\left(\frac{dy}{dx}\right)^3 = 0$	(IV) 4

2026: 29 May Shift 1

Match List-I with List-II

List-I (Differential equation)	List-II (Integrating factor)
(A) $\dfrac{xdy}{dx}-y=x^2e^x$	(I) $x$
(B) $\dfrac{dy}{dx}-2y=e^x$	(II) $x^4$
(C) $\dfrac{xdy}{dx}+y=1$	(III) $\dfrac{1}{x}$
(D) $\dfrac{xdy}{dx}+4y=x^4$	(IV) $e^{-2x}$

Choose the correct answer from the options given below:

Solution