The order and the degree of the differential equation d^2y/dx^2 + x(dy/dx)^2 = 2x^2 (d^2y/dx^2) are respectively: Option 1: 2 and 1 Option 2: 2 and 2 Option 3: 2 and 3 Option 4: 2 and not defined

Answer: 2 and not defined. Solution: Highest order derivative is d^2y/dx^2, so order = 2. Since d^2y/dx^2 appears inside a logarithm, the equation cannot be expressed as a polynomial in derivatives. Hence degree is not defined.

Calculus

Differential Equations

Medium

The order and the degree of the differential equation $\frac{d^2y}{dx^2} + x\left(\frac{dy}{dx}\right)^2 = 2x^2 \log\left(\frac{d^2y}{dx^2}\right)$ are respectively:

2 and 1

2 and 2

2 and 3

2 and not defined

✅ Correct Option: 4

Highest order derivative is $\frac{d^2y}{dx^2}$ , so order = 2. Since $\frac{d^2y}{dx^2}$ appears inside a logarithm, the equation cannot be expressed as a polynomial in derivatives. Hence degree is not defined.

2026: 25 May Shift 1

General solution of the differential equation $\dfrac{3ydx - 2xdy}{y} = 0$ is :

[where $c$ is an arbitrary constant]

2022: 10 Aug Shift 1

The solution of differential equation $\sqrt{x+1} - \sqrt{x-1}\frac{dy}{dx} = 0$ is

2022: 30 Aug Shift 1

Solution of the differential equation $(x + xy)dy - y(1 - x^2)dx = 0$ is

2025: 21 May Shift 1

Match List-I with List-II

List-I	List-II
Differential Equation	General solution
---	---
(A) $\dfrac{dy}{dx} = \dfrac{y}{x}; x \neq 0$	(I) $y = cx; c \text{ is an arbitrary constant}$
(B) $x dx - y dy = 0; y \neq 0, x \neq 0$	(II) $x^2 - y^2 = c; c \text{ is an arbitrary constant}$
(C) $\dfrac{(x^2 - 1)}{y^2 + 1}\dfrac{dx}{dy} = 1$	(III) $2x + 3y = c; c \text{ is an arbitrary constant}$
(D) $2 dx + 3 dy = 0$	(IV) $(x^3-y^3) = c + 3(x+y); c \text{ is an arbitrary constant}$

Choose the correct answer from the options given below:

2026: 29 May Shift 2

In reference to the differential equation : $y''+y=(e)^{y'}$ , which of the following statements are correct ?

A. The order of the differential equation is 1.

B. The degree of the differential equation is 1.

C. The order of the differential equation is 2.

D. The degree of the differential equation is not defined.

Choose the correct answer from the options given below:

2023: 22 May Shift 3

The differential equation of the family of curves $y = a \sin(bx + c)$ , a and c are parameters, is :

The order and the degree of the differential equation d2ydx2+x(dydx)2=2x2log⁡(d2ydx2)\frac{d^2y}{dx^2} + x\left(\frac{dy}{dx}\right)^2 = 2x^2 \log\left(\frac{d^2y}{dx^2}\right)dx2d2y​+x(dxdy​)2=2x2log(dx2d2y​) are respectively:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The order and the degree of the differential equation $\frac{d^2y}{dx^2} + x\left(\frac{dy}{dx}\right)^2 = 2x^2 \log\left(\frac{d^2y}{dx^2}\right)$ are respectively: