The order and degree of the differential equation [(d^2y/dx^2)^2 - 3]^(1/3) = 2(dy/dx)^(1/4) are Option 1: order = 2, degree = 2 Option 2: order = 2, degree = 4 Option 3: order = 2, degree = 8 Option 4: order = 1, degree = 1

Answer: order = 2, degree = 8. Solution: [(d^2y/dx^2)^2 - 3]^(1/3) = 2(dy/dx)^(1/4). To make all derivative powers integer, raise both sides to the 12th power. Equivalently, the LHS becomes [(d^2y/dx^2)^2 - 3]^4 and the RHS becomes 2^12(dy/dx)^3. Highest derivative is d^2y/dx^2, so order =2. Highest power of this derivative after rationalisation is 2x 4 = 8, so degree = 8.

Calculus

Differential Equations

Hard

The order and degree of the differential equation $\left[\left(\frac{d^2y}{dx^2}\right)^2 - 3\right]^{\frac{1}{3}} = 2\left(\frac{dy}{dx}\right)^{\frac{1}{4}}$ are

order = 2, degree = 2

order = 2, degree = 4

order = 2, degree = 8

order = 1, degree = 1

✅ Correct Option: 3

$\left[\left(\frac{d^2y}{dx^2}\right)^2 - 3\right]^{1/3} = 2\left(\frac{dy}{dx}\right)^{1/4}$ .

To make all derivative powers integer, raise both sides to the 12th power. Equivalently, the LHS becomes $\left[\left(\frac{d^2y}{dx^2}\right)^2 - 3\right]^4$ and the RHS becomes $2^{12}\left(\frac{dy}{dx}\right)^3$ .

Highest derivative is $\frac{d^2y}{dx^2}$ , so order $=2$ . Highest power of this derivative after rationalisation is $2\times 4 = 8$ , so degree $= 8$ .

2022: 4 Aug Shift 1

The solution of the differential equation $\frac{dy}{dx} = \frac{\lambda^2}{(x+y)^2}$ ( $\lambda$ is constant) is:

2022: 6 Aug Shift 2

Match List I with List II

List I	List II
A. The number of arbitrary constants in the particular solution of differential equation of order 2	I. 1
B. The number of arbitrary constants in the general solution of differential equation of order 2	II. 0
C. The integrating factor of differential equation $\frac{dy}{dx} + \frac{1}{x}y = 3, x > 0$ , is	III. 2
D. For differential equation, $x^2 \frac{dy}{dx} + x = xy, x > 0, \lim_{x \to 0^+} y(x)$ is equal to	IV. $x$

Choose the correct answer from the options given below:

2026: 12 May Shift 2

Match List-I with List-II

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

Choose the correct answer from the options given below:

2026: 31 May Shift 2

If $m$ and $n$ are respectively order and degree of the differential equation

$\left(\dfrac{d^2y}{dx^2}\right)^5 + 6\cdot\dfrac{\left(\dfrac{d^2y}{dx^2}\right)^3}{\dfrac{d^3y}{dx^3}} + \dfrac{d^3y}{dx^3} = x^2+5$ then :

2025: 30 May Shift 1

The solution of the differential equation $\log_e\left(\frac{dy}{dx}\right) = 5x + 2y$ is given by

2023: 30 May Shift 3

Solution of differential equation $x dy - y dx = 0$ respresents :

The order and degree of the differential equation [(d2ydx2)2−3]13=2(dydx)14\left[\left(\frac{d^2y}{dx^2}\right)^2 - 3\right]^{\frac{1}{3}} = 2\left(\frac{dy}{dx}\right)^{\frac{1}{4}}[(dx2d2y​)2−3]31​=2(dxdy​)41​ are

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CUET Mathematics Past Year Questions (Topic-Wise)

The order and degree of the differential equation $\left[\left(\frac{d^2y}{dx^2}\right)^2 - 3\right]^{\frac{1}{3}} = 2\left(\frac{dy}{dx}\right)^{\frac{1}{4}}$ are