The degree of the differential equation (2 + (dy/dx)^2)^(3/2) = a^2 d^2y/dx^2 is: Option 1: 6 Option 2: 1 Option 3: 3 Option 4: 2

Answer: 2. Solution: The degree of a differential equation is the highest power of the highest order derivative when the equation is in polynomial form (no roots, no fractions with derivatives). Given equation: (2 + (dy/dx)^2)^(3/2) = a^2 d^2y/dx^2 The highest order derivative in the equation is d^2y/dx^2 (second order). The left side has a fractional power 3/2, so the equation is not in polynomial form. Squaring both sides: [(2 + (dy/dx)^2)^(3/2)]^2 = [a^2 d^2y/dx^2]^2 (2 + (dy/dx)^2)^3 = a^4 (d^2y/dx^2)^2 The equation is now in polynomial form. The highest order derivative d^2y/dx^2 appears with power 2. Therefore, the degree of the differential equation is 2.

Calculus

Differential Equations

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The degree of the differential equation $\left(2 + \left(\frac{dy}{dx}\right)^2\right)^{\frac{3}{2}} = a^2 \frac{d^2y}{dx^2}$ is:

✅ Correct Option: 4

The degree of a differential equation is the highest power of the highest order derivative when the equation is in polynomial form (no roots, no fractions with derivatives).

Given equation:

$\left(2 + \left(\frac{dy}{dx}\right)^2\right)^{\frac{3}{2}} = a^2 \frac{d^2y}{dx^2}$

The highest order derivative in the equation is $\frac{d^2y}{dx^2}$ (second order).

The left side has a fractional power $\frac{3}{2}$ , so the equation is not in polynomial form.

Squaring both sides:

$\left[\left(2 + \left(\frac{dy}{dx}\right)^2\right)^{\frac{3}{2}}\right]^{2} = \left[a^2 \frac{d^2y}{dx^2}\right]^{2}$

$\left(2 + \left(\frac{dy}{dx}\right)^2\right)^3 = a^4 \left(\frac{d^2y}{dx^2}\right)^{2}$

The equation is now in polynomial form.

The highest order derivative $\frac{d^2y}{dx^2}$ appears with power $2$ .

Therefore, the degree of the differential equation is $2$ .

2025: 13 May Shift 1

Let the degree and order of the differential equation $2x^3\frac{dy}{dx}-5\left(\frac{d^2y}{dx^2}\right)^2=6\left(\frac{dy}{dx}\right)^3$ be $m$ and $n$ respectively. Then

(A) m = 2

(B) n = 3

(D) mn = 4

Choose the correct answer from the options given below:

2026: 30 May Shift 2

Match List-I with List-II

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

Choose the correct answer from the options given below:

2025: 26 May Shift 2

In the following differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 = 2x^2 \log\left(\frac{d^2y}{dx^2}\right)$ order and degree is:

2023: 15 June Shift 2

The differential equation whose solution is $Ax^2 + By^2 = 1$ where A and B are arbitrary constant is of :

(A) first order and first degree

(B) second order and first degree

(D) second order

Choose the correct answer from the options given below :

2025: 22 May Shift 1

The differential equation of the family of curves $y = Ae^{3x} + Be^{-3 x}$ , where $a$ and $\beta$ are arbitrary constants, is

2024: 16 May Shift 1

The degree of the differential equation $\left(1-\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}=k \frac{d^{2} y}{d x^{2}}$ is :

The degree of the differential equation (2+(dydx)2)32=a2d2ydx2\left(2 + \left(\frac{dy}{dx}\right)^2\right)^{\frac{3}{2}} = a^2 \frac{d^2y}{dx^2}(2+(dxdy​)2)23​=a2dx2d2y​ is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The degree of the differential equation $\left(2 + \left(\frac{dy}{dx}\right)^2\right)^{\frac{3}{2}} = a^2 \frac{d^2y}{dx^2}$ is: