Calculus

Differential Equations

Medium

Match List - I with List - II

List - I (Differential Equation) List - II (Degree)
A. $\left[1 + (y')^2\right]^2 = y''$ I. $2$
B. $\left[1 + (y'')^3\right]^{\frac{1}{2}} = (y')^3$ II. $4$
C. $(y''')^2 + y'' + 3y' + 5y = e^x$ III. $1$
D. $\left[1 + (y')^3\right]^{\frac{1}{2}} = (y'')^2$ IV. $3$

Choose the correct answer from the option given below:

List - I (Differential Equation)	List - II (Degree)
A. $\left[1 + (y')^2\right]^2 = y''$	I. $2$
B. $\left[1 + (y'')^3\right]^{\frac{1}{2}} = (y')^3$	II. $4$
C. $(y''')^2 + y'' + 3y' + 5y = e^x$	III. $1$
D. $\left[1 + (y')^3\right]^{\frac{1}{2}} = (y'')^2$	IV. $3$

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

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

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

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

✅ Correct Option: 2

A: $[1+(y')^2]^2 = y''$ , degree of $y''$ is $1$ (III). B: square both sides: $1+(y'')^3 = (y')^6$ , degree of $y''$ is $3$ (IV). C: highest order $y'''$ , degree $2$ (I). D: square: $1+(y')^3 = (y'')^4$ , degree of $y''$ is $4$ (II). Match: A-III, B-IV, C-I, D-II.

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 $\log x=\log_e x$ )

2026: 26 May Shift 2

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x+2}{3-y}, (y \neq 3), y(0) = 0$

represents

2025: 21 May Shift 1

The number of arbitrary constants in the general solution of a differential equation with degree 1 and order 3, is

2025: 15 May Shift 2

The general solution of the differential equation $(x^2 - yx^2)dy + (y^2 + x^2y^2)dx = 0$ is:

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

Choose the correct answer from the options given below:

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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